Abstract

By analyzing the interaction of a few-cycle laser pulse within an asymmetric semiconductor double quantum well structure, we show that the transient coherence thus produced is strongly dependent on the carrier-envelope-phase (CEP) and significantly enhanced due to the Fano-type interference. A method to determine the CEP is proposed by directly mapping the CEP dependent coherence to the quantum beat signals.

©2009 Optical Society of America

There have been significant research activities on quantum coherence and interference phenomena induced by the intersubband transitions (ISBT) of semiconductor quantum wells (QW) in the last decades [1, 2]. A number of fascinating coherence introduced effects have been discovered when lasers are applied to the QW structures, such as tunneling induced transparency [3, 4], electromagnetically induced transparency [5, 6, 7, 8], gain without inversion [9], coherent control of electron population [10], Autler-Townes splitting [11], and terahertz emission [12]. These studies have considerably modified our understandings of the nature and consequences of quantum coherence on the quantum and nonlinear optical processes in QW systems [13, 14, 15]. Recently, the effects of the carrier-envelope phase (CEP) of few-cycle pulses on the quantum coherence and interference in optical media have drawn lots of attentions [16, 17, 18, 19, 20, 21, 22], due to that these investigations can lead to many practical applications in extracting the related information of an ultrashort laser pulse.

In this letter, we theoretically investigate the effects of CEP on the transient coherence produced by an ultrashort laser pulse of a few cycles in an asymmetric double quantum well structures. We demonstrate that the coherent effect is strongly dependent on the CEP, and the magnitude of transient coherence can be enhanced significantly due to the Fano-type interference. We also show that the coherence thus produced can also be mapped into the signal of quantum beats and hence might be used to determine the CEP of few-cycle pulses.

The schematic energy-level diagram of a GaAs/AlxGa1-xAs coupled quantum well structure are shown in Fig. 1(a): a AlxGa1-xAs shallow well and a GaAs deep well separated by a thick AlyGa1-yAs tunnel barrier. This barrier will couple the excited state of deep well with the ground state of shallow well to create a doublet states |2〉 and |3〉. One external light field is used to illuminate the system, and acts both on the transitions |1〉↔ |3〉 and |1〉↔|2〉 simultaneously. Tunneling to a continuum of energies takes place from states |2〉 and |3〉 through the thin barrier on the right of the deep well. The probability amplitude for the absorption of a photon can be thought as the superposition of two absorption paths, one via level |2〉 and one via level |3〉, both decaying by tunneling to the same continuum. Fano-type destructive interference between the two absorption paths may then occur so as to cancel the absorption altogether. Nearly vanishing absorptions due to the Fano effect have already been predicted [23] and observed [3, 4, 24]. As shown in Fig. 1(b), we consider an ultrashort optical pulse of the electric field E(t)=-∂A(t)/∂t with the vector potential A(t)=A0e(t2τ)2τ2sin(ωt+ϕ) [16, 17, 18, 19], where A 0, τ,ω, and ϕ are the amplitude, pulse width, carrier-envelope frequency, and the phase of the vector potential, respectively. Let us assume that the electronic wave function in the form of |ψ〉=a 1|1〉+a 2|2〉+a 3|3〉, then the time evolution equation for |ψ〉 is governed by the Schrödinger equation, with which we can have the corresponding differential equations for the probability amplitudes aj as follows:

a.1=iΩξ(t)[a2(t)eiΔt+qa3ei(Δ+δ)t],
a.2=γ2a2+iΩξ(t)a1eiΔt+pγ2γ3a3eiδt,
a.3=γ3γ3+iΩξ(t)qa1ei(Δ+δ)t+pγ2γ3a2eiδt,

where ξ(t)=ω1[e(t2τ)2τ2sin(ωt+ϕ)]t, the dot overhead means the derivative with respect to time. qΩ=qΩ*= 12 ωA 0/(2h̄) is the half Rabi frequency for the transition |1〉↔|j〉 (j=2, 3), with q being the ratio of the dipole matrix element between two upper levels. 2δ is the energy splitting due to the tunneling between the upper levels and Δ=ω0 is the detuning between the frequency of the ultrashort pulse and the average transition frequency ω 0=(ω32)/2, where ω 2 and ω 3 being the transition frequencies corresponding to |2〉↔|1〉 and |3〉↔|1〉, respectively. The decay rates have been added phenomenologically in the above equations (1–3), where γ 2,3=γ2l,3l+γ2d,3d denotes the total decay rate of the upper states including both the population scattering rates γ2l,3l due to longitudinal optical (LO) phonon emission events at low temperature and the dephasing rates γ2d,3d due to a combination of quasielastic interface roughness scattering or acoustic phonon scattering. Besides, we have neglected other inhomogeneous broadening effects due to their small influences[25]. Moreover, pγ2γ3=γ2lγ3l represents the cross-coupling of the two upper states via the LO phonon decay[3, 4], which arises from the tunneling to the continuum through the thin barrier next to the deep well. Here we use p to assess the cross coupling strength[26, 27, 28, 29, 30], where the limit values p=0 and p=1 correspond, respectively, to no interference and perfect interference.

 figure: Fig. 1.

Fig. 1. (a) Schematic diagram of our proposed GaAs/AlxGa1-xAs QW structure illuminated by an ultrashort few-cycle laser pulse in (b), where the electric field E(t) of the ultrashort pulse versus time t is shown for ϕ=π/2.

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 figure: Fig. 2.

Fig. 2. The transient coherence ρ 23×104 versus the CEP, ϕ, (solid curves for the real part; dashed curves for the imaginary part; and dotted curves for the absolute value, respectively) at the time t=4τ for different widths, τ, and Rabi frequencies, Ω, of the pulse with other parameters h̄ω=125 meV, q=1.2, Δ=0, 2δ=7.6 meV, γ2l=5.6 meV, γ3l=7.0 meV, γ2d=4.13 meV, and γ3d=5.35 meV.

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As an example for the numerical calculations, we consider the structure design of the asymmetric double quantum-well: a 68 Å thick Al0.15Ga0.85As shallow well and a 70 Å thick GaAs deep well separated by a 20 Å thick Al0.3Ga0.7As tunnel barrier. The doublet states (|2〉 and |3〉) are both coupled to the continuum by a 15 Å thin Al0.3Ga0.7As barrier, which produces the decay-induced coherence. Note that, for temperature up to 10 K with electron sheet densities smaller than 1012 cm-2, the dephasing rates γid can be estimated [3] to be γ2d=4.13 meV and γ3d=5.35 meV. The population-decay rates can be calculated [31]: upon solving the effective mass Schrödinger equation with outgoing waves at infinity, we obtain a set of complex eigenvalues whose real and imaginary parts yield, respectively the quasibound state energy levels and resonance widths. For our asymmetric double quantum well structure, the population-decay rates turn out to be γ2l=5.6 meV and γ3l=7.0 meV. In such a scenario, a coupling ultrashort laser can produce the oscillation between the doublet states. Sequentially the induced oscillation is strongly dependent on the CEP of a few-cycle pulse, which produce a CEP dependent transient coherence for |ρ23|=|a 2(t)a*3(t)|. Direct numerical calculations for the solutions of Eqs. (1–3) demonstrate that the CEP of ultrashort laser pulses with only a few cycles has indeed significant effects on the coherence ρ 23 in the weak field regime (α=Ω/ω≪1). Figure 2 illustrates this point via some typical examples. The real, imaginary, and absolute values of the transient coherence ρ 23 is shown with the dependence of the CEP (ϕ) at the time t=4τ for two different pulse widths (τ=9/ω, τ=18/ω) and for two different Rabi frequencies (Ω=ω/20, Ω=ω/5), under the initial conditions a 1(0)=1 and a 2(0)=a 3(0)=0.

This result can be explained physically by the time-dependent perturbation theory with a small parameter α≪1. Under the initial conditions a 2,3(0)=0 and a 1(0)=1, taking aj=∑ka(k)j with a(k)j=𝒪(αk), we can see from Eqs. (1–3) that a 2,3(t)=𝒪(α) and a 1(t)=𝒪(α0), thus ρ 23=𝒪(α2). Clearly CEP dependence has been produced even for the low Rabi frequency i.e., Ω=ω/20. Just as shown in Fig. 2, the dependent amplitude become pronounced as the Rabi frequency increases and the pulse width becomes narrow. The low Rabi frequencies induce less transient coherence and hence are obviously non-favorable from the viewpoint of the experimental measurement. The lower limit for Rabi frequency depends on the precision of the technique in measurement. With state-of-the-art technologies to handle the weak light-QW interaction, relative effects of the QW system considered here can be measured in low temperature (10 K) [2]. Besides, we note that α~E characterizes the electric field E(t) with the period 2π for the CEP ϕ. In such a case, the relation ρ 23=𝒪(α 2) implies that ρ 23 should approximately have the period π, as illustrated in Fig. 2.

 figure: Fig. 3.

Fig. 3. The transient coherence |ρ 23|×104 versus the CEP ϕ for the case of (a, c) p=0 and (b, d) p=1 at the time t=4τ for different widths, τ, and Rabi frequencies, Ω, of the pulse with other parameters h̄ω=125 meV, q=1.2, Δ=0, 2δ=17.6 meV, γ2l=0.31 meV, γ3l=0.26 meV, γ2d=0.031 meV, and γ3d=0.026 meV.

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It should be noted that the interference induced by the resonant tunneling have been included in plotting Fig. 2. According to the decay-rate values (γ2l=5.6 meV, γ3l=7.0 meV, γ2d=4.13 meV, and γ3d=5.35 meV), we can obtain the cross coupling strength between |2〉 and |3〉 p=0.54. In order to examine the effect of the interference induced by the resonant tunneling on the CEP dependent coherence, we consider a similar GaAs/AlGaAs asymmetric double quantum well structure consists of two quantum wells (55 Å Al0.3Ga0.7As shallow well and 57 Å GaAs deep well) separated by a 35 Å Al0.5Ga0.5As tunneling barrier. Aluminum is added to the shallow well in order to reduce the contribution of interface roughness scattering. The energy splitting between the upper levels is calculated to be 2δ=7.6 meV. For a sheet carrier density of 1012 cm-2 in the quantum wells, we can obtain the LO-phonon decay rates γ2l=0.31 meV and γ3l=0.26 meV, and the dephasing rates can be estimated to be γ2d=0.031 and γ3d=0.026 meV. Thus, the cross coupling strength is estimated as p=0.90. This is close to the ideal value p=1 and corresponds to a large tunneling efficiency leading to a strong Fano-type interference effect. With new parameter values of this QW structure, we show in Fig. 3 the transient coherence |ρ 23| versus the CEP ϕ at the time t=4τ under the same initial conditions as in Fig. 2, and it demonstrates that the amplitude of the transient coherence is enhanced. This interesting result is produced from the perfectly interference induced by the resonant tunneling. The large amplitude is obviously favorable from the viewpoint of the experimental measurement in the weak-field regime. More interestingly, the parameters of the electron subbands in QWstructures can be engineered to give a desired amplitude of coherence by utilizing so-called structure coherent control in design [2].

We now study the quantum beats due to the coherence ρ23 produced by a few-cycle ultrafast pulse for the time interval T>t with the initial time t=t 0=4τ. The quantum beat note signal I can be given as [32]

I=ψ(T)Ê1()(T)Ê2(+)(T)ψ(T)+c.c.,

with the state of our system |ψ(T)〉 satisfying |ψ(T)〉=∑jaj|j,0〉+b 2|1,1ω21〉+b 3|1,1ω31〉. Here |n,0〉, |1,1ω j1〉 describe the levels |n〉(n=1,2, 3) with no photon, and ground state |1〉 with one photon in the field mode j characterizing the transition |0〉→| j〉(j=2, 3), respectively. Ê1()(T)=1â1eiω21(Tt) and Ê2(+)(T)=2â2e31(Tt) denote the electric field per photon for the mode j. Inserting Hamiltonian H=h̄∑jgj(âj|j〉〈1|+â j|1〉〈j|) into the Schrödinger equation, i.e. |ψ(T)〉/∂T=-i(H/h̄)|ψ(T)〉, we obtain

i(ddT+γj)ajpγ2γ3(a3δj,2+a2δj,3)=gjbj,
idbjdTgjaj=0,j=2,3,

with gj0 jj/(2h̄). By solving Eqs. (5,6) under the initial conditions of b 1,2(t)=0, the quantum beat signals can be calculated as

I=I0(ϕ)cos[2δ(Tt)+η(t)],

where I 0(ϕ)=C|ρ 23(t)| with the coefficient C being determined by j, gj, γj, and p. And η(t) is an adjustable phase shift of the ultrashort pulse at the time instant T=t. Here we have used the assumption of γj, pγ2γ32gj, so that we can neglected the time-dependent term in the coefficient C. From Eq. (7), we find that I 0(ϕ) depends on the CEP ϕ through the CEP dependent coherence |ρ 23(t)| as shown in Fig. 2. Thus the CEP of a few-cycle pulse might be determined by measuring the quantum beat signals. By defining the depth of modulation, M, in the signal amplitude of quantum beats as M=2[I 0(ϕ)max-I 0(ϕ)min]/[I 0(ϕ)max+I 0(ϕ)min], with I 0(ϕ)max,min being the maximum (minimum) amplitude. For a certain value of C, one can have a much larger value of the modulation depth M in our system than those proposed in the previous schemes [16, 17, 18], as illustrated in Fig. 2.

In conclusion, we have studied the generation of transient coherence induced by few-cycle laser pulses in an asymmetric semiconductor double QW structure, and shown that the coherence thus produced strongly depends on the carrier-envelope phase of the ultrashort laser pulses. Importantly, the amplitude of the CEP dependent transient coherence can be greatly enhanced due to the Fano-type interference. Besides, we also shown that the CEP-dependent coherence can be mapped into the signal of quantum beats, thus one can determine the CEP by measuring the quantum beat signals. We believe that the CEP dependent coherence in our proposed QW structure will also manifest itself in other quantum interference phenomena as well, and hence our study might open up an avenue to explore and utilize the CEP dependent coherent effects and could be exploited in real solid-state devices as high speed optical modulators and switches.

This work is supported by National Natural Science Foundation (NSF) of China under Grants No. 10704017 and No. 10874050, and also partially supported by the National Basic Research Program of China (973 program), Grant No. 2007CB936300 and No. 2005CB724508. We thank Prof. Y. Wu and Ite. Yu for their helpful discussions.

References and links

1. Z. Ficek and S. Swain, Quantum Interference and Coherence (Springer, New York, 2004).

2. H.C. Liu and F. Capasso, Intersubband Transitions in Quantum Wells: Physics and Device Applications (Academic Press, San Diego, 2000).

3. H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoğlu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).

4. J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).

5. G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000). [PubMed]  

6. L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).

7. T. Müller, W. Parz, G. Strasser, and K. Unterrainer, “Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well,” Phys. Rev. B 70, 155324(1–5) (2004).

8. S. M. Sadeghi, S. R. Leffler, and J. Meyer, “Quantum interference and nonlinear optical processes in the conduction bands of infrared-coupled quantum wells,” Phys. Rev. B 59, 15388–15394 (1999).

9. M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).

10. E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semicondutor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).

11. J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).

12. B. S. Williams, B. Xu, Q. Hu, and M. R. Melloch, “Narrow-linewidth terahertz intersubband emission from three-level systems,” Appl. Phys. Lett. 75, 2927–2929 (1999).

13. T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

14. K. A. Pronin and A. D. Bandrauk, “Coherent Control of Harmonic Generation in Superlattices: Single-Mode Response,” Phys. Rev. Lett. 97, 020602(1–4) (2006).

15. C. Van Vlack and S. Hughes, “Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors,” Phys. Rev. Lett. 98, 167404(1–4) (2007).

16. T. Nakajima and S. Watanabe, “Effects of the carrier-encelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96, 213001(1–4) (2006).

17. T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31, 1920–1922 (2006). [PubMed]  

18. Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76, 013832(1–4) (2007).

19. Y. Wu and X. Yang, “Strong-Coupling Theory of Periodically Driven Two-Level Systems,” Phys. Rev. Lett. 98, 013601(1–4) (2007).

20. G. L. Kamta and A. D. Bandrauk, “Phase Dependence of Enhanced Ionization in Asymmetric Molecules,” Phys. Rev. Lett. 94, 203003(1–4) (2005).

21. W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).

22. C. Zhang, X. Song, W. Yang, and Z. Xu, “Carrier-envelope phase control of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well,” Opt. Express 16, 11487–1496 (2008).

23. H. Schmidt and A. Imamoglu, “Nonlinear optical devices based on a transparency in semiconductor intersubband transitions,” Opt. Commun. 131, 333–338 (1996).

24. J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

25. I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

26. E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).

27. E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency of a short laser pulse via decay interference in a closed V-type system,” Phys. Rev. A 61, 045802(1–4) (1999).

28. J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

29. W. X. Yang and R.-K. Lee, “Controllable entanglement and polarization phase gate in coupled double quantum-well structures,” Opt. Express 16, 17161–17170 (2008). [PubMed]  

30. W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).

31. D. Ahn and S. L. Chuang, “Exact calculations of quasibound states of an isolated quantum well with uniform electric field: Quantum-well stark resonance,” Phys. Rev. B 34, 9034–9037 (2008).

32. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).

References

  • View by:

  1. Z. Ficek and S. Swain, Quantum Interference and Coherence (Springer, New York, 2004).
  2. H.C. Liu and F. Capasso, Intersubband Transitions in Quantum Wells: Physics and Device Applications (Academic Press, San Diego, 2000).
  3. H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoğlu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
  4. J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).
  5. G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000).
    [PubMed]
  6. L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
  7. T. Müller, W. Parz, G. Strasser, and K. Unterrainer, “Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well,” Phys. Rev. B 70, 155324(1–5) (2004).
  8. S. M. Sadeghi, S. R. Leffler, and J. Meyer, “Quantum interference and nonlinear optical processes in the conduction bands of infrared-coupled quantum wells,” Phys. Rev. B 59, 15388–15394 (1999).
  9. M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).
  10. E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semicondutor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
  11. J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).
  12. B. S. Williams, B. Xu, Q. Hu, and M. R. Melloch, “Narrow-linewidth terahertz intersubband emission from three-level systems,” Appl. Phys. Lett. 75, 2927–2929 (1999).
  13. T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).
  14. K. A. Pronin and A. D. Bandrauk, “Coherent Control of Harmonic Generation in Superlattices: Single-Mode Response,” Phys. Rev. Lett. 97, 020602(1–4) (2006).
  15. C. Van Vlack and S. Hughes, “Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors,” Phys. Rev. Lett. 98, 167404(1–4) (2007).
  16. T. Nakajima and S. Watanabe, “Effects of the carrier-encelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96, 213001(1–4) (2006).
  17. T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31, 1920–1922 (2006).
    [PubMed]
  18. Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76, 013832(1–4) (2007).
  19. Y. Wu and X. Yang, “Strong-Coupling Theory of Periodically Driven Two-Level Systems,” Phys. Rev. Lett. 98, 013601(1–4) (2007).
  20. G. L. Kamta and A. D. Bandrauk, “Phase Dependence of Enhanced Ionization in Asymmetric Molecules,” Phys. Rev. Lett. 94, 203003(1–4) (2005).
  21. W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).
  22. C. Zhang, X. Song, W. Yang, and Z. Xu, “Carrier-envelope phase control of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well,” Opt. Express 16, 11487–1496 (2008).
  23. H. Schmidt and A. Imamoglu, “Nonlinear optical devices based on a transparency in semiconductor intersubband transitions,” Opt. Commun. 131, 333–338 (1996).
  24. J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).
  25. I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
  26. E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).
  27. E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency of a short laser pulse via decay interference in a closed V-type system,” Phys. Rev. A 61, 045802(1–4) (1999).
  28. J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
  29. W. X. Yang and R.-K. Lee, “Controllable entanglement and polarization phase gate in coupled double quantum-well structures,” Opt. Express 16, 17161–17170 (2008).
    [PubMed]
  30. W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
  31. D. Ahn and S. L. Chuang, “Exact calculations of quasibound states of an isolated quantum well with uniform electric field: Quantum-well stark resonance,” Phys. Rev. B 34, 9034–9037 (2008).
  32. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).

2008 (4)

C. Zhang, X. Song, W. Yang, and Z. Xu, “Carrier-envelope phase control of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well,” Opt. Express 16, 11487–1496 (2008).

W. X. Yang and R.-K. Lee, “Controllable entanglement and polarization phase gate in coupled double quantum-well structures,” Opt. Express 16, 17161–17170 (2008).
[PubMed]

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).

D. Ahn and S. L. Chuang, “Exact calculations of quasibound states of an isolated quantum well with uniform electric field: Quantum-well stark resonance,” Phys. Rev. B 34, 9034–9037 (2008).

2007 (4)

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).

C. Van Vlack and S. Hughes, “Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors,” Phys. Rev. Lett. 98, 167404(1–4) (2007).

Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76, 013832(1–4) (2007).

Y. Wu and X. Yang, “Strong-Coupling Theory of Periodically Driven Two-Level Systems,” Phys. Rev. Lett. 98, 013601(1–4) (2007).

2006 (5)

T. Nakajima and S. Watanabe, “Effects of the carrier-encelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96, 213001(1–4) (2006).

T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31, 1920–1922 (2006).
[PubMed]

K. A. Pronin and A. D. Bandrauk, “Coherent Control of Harmonic Generation in Superlattices: Single-Mode Response,” Phys. Rev. Lett. 97, 020602(1–4) (2006).

M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semicondutor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).

2005 (3)

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).

G. L. Kamta and A. D. Bandrauk, “Phase Dependence of Enhanced Ionization in Asymmetric Molecules,” Phys. Rev. Lett. 94, 203003(1–4) (2005).

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

2004 (3)

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

T. Müller, W. Parz, G. Strasser, and K. Unterrainer, “Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well,” Phys. Rev. B 70, 155324(1–5) (2004).

2002 (1)

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).

2000 (1)

G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000).
[PubMed]

1999 (4)

B. S. Williams, B. Xu, Q. Hu, and M. R. Melloch, “Narrow-linewidth terahertz intersubband emission from three-level systems,” Appl. Phys. Lett. 75, 2927–2929 (1999).

S. M. Sadeghi, S. R. Leffler, and J. Meyer, “Quantum interference and nonlinear optical processes in the conduction bands of infrared-coupled quantum wells,” Phys. Rev. B 59, 15388–15394 (1999).

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency of a short laser pulse via decay interference in a closed V-type system,” Phys. Rev. A 61, 045802(1–4) (1999).

1997 (3)

J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoğlu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).

J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).

1996 (1)

H. Schmidt and A. Imamoglu, “Nonlinear optical devices based on a transparency in semiconductor intersubband transitions,” Opt. Commun. 131, 333–338 (1996).

Ahn, D.

D. Ahn and S. L. Chuang, “Exact calculations of quasibound states of an isolated quantum well with uniform electric field: Quantum-well stark resonance,” Phys. Rev. B 34, 9034–9037 (2008).

Artoni, M.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

Bandrauk, A. D.

K. A. Pronin and A. D. Bandrauk, “Coherent Control of Harmonic Generation in Superlattices: Single-Mode Response,” Phys. Rev. Lett. 97, 020602(1–4) (2006).

G. L. Kamta and A. D. Bandrauk, “Phase Dependence of Enhanced Ionization in Asymmetric Molecules,” Phys. Rev. Lett. 94, 203003(1–4) (2005).

Bassani, F.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).

Beck, M.

M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).

Bhat, R. D. R.

T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

Campman, K. L.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoğlu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).

Capasso, F.

J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).

J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

H.C. Liu and F. Capasso, Intersubband Transitions in Quantum Wells: Physics and Device Applications (Academic Press, San Diego, 2000).

Cheng, Y.

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).

Chuang, S. L.

D. Ahn and S. L. Chuang, “Exact calculations of quasibound states of an isolated quantum well with uniform electric field: Quantum-well stark resonance,” Phys. Rev. B 34, 9034–9037 (2008).

Cundiff, S. T.

T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

Czajkowski, G.

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).

Davoudi, B.

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).

Dynes, J. F.

M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).

Elsaesser, T.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Faist, J.

M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).

J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).

J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

Ficek, Z.

Z. Ficek and S. Swain, Quantum Interference and Coherence (Springer, New York, 2004).

Förstner, J.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Frogley, M. D.

M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).

Frontier, T. M.

T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

Gao, J. Y.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

Gong, S.

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).

Gossard, A. C.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoğlu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).

Hey, R.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Hou, J. M.

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).

Hu, Q.

B. S. Williams, B. Xu, Q. Hu, and M. R. Melloch, “Narrow-linewidth terahertz intersubband emission from three-level systems,” Appl. Phys. Lett. 75, 2927–2929 (1999).

Hughes, S.

C. Van Vlack and S. Hughes, “Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors,” Phys. Rev. Lett. 98, 167404(1–4) (2007).

Hutchinson, A. L.

J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

Imamoglu, A.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoğlu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).

H. Schmidt and A. Imamoglu, “Nonlinear optical devices based on a transparency in semiconductor intersubband transitions,” Opt. Commun. 131, 333–338 (1996).

Jones, D. J.

T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

Kaindl, R. A.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Kamta, G. L.

G. L. Kamta and A. D. Bandrauk, “Phase Dependence of Enhanced Ionization in Asymmetric Molecules,” Phys. Rev. Lett. 94, 203003(1–4) (2005).

Knight, P. L.

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency of a short laser pulse via decay interference in a closed V-type system,” Phys. Rev. A 61, 045802(1–4) (1999).

Knorr, A.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Kylstrra, N. J.

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency of a short laser pulse via decay interference in a closed V-type system,” Phys. Rev. A 61, 045802(1–4) (1999).

La Rocca, G. C.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

Lee, R.-K.

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).

W. X. Yang and R.-K. Lee, “Controllable entanglement and polarization phase gate in coupled double quantum-well structures,” Opt. Express 16, 17161–17170 (2008).
[PubMed]

Lee, S.-C.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Leffler, S. R.

S. M. Sadeghi, S. R. Leffler, and J. Meyer, “Quantum interference and nonlinear optical processes in the conduction bands of infrared-coupled quantum wells,” Phys. Rev. B 59, 15388–15394 (1999).

Liu, H.C.

H.C. Liu and F. Capasso, Intersubband Transitions in Quantum Wells: Physics and Device Applications (Academic Press, San Diego, 2000).

Melloch, M. R.

B. S. Williams, B. Xu, Q. Hu, and M. R. Melloch, “Narrow-linewidth terahertz intersubband emission from three-level systems,” Appl. Phys. Lett. 75, 2927–2929 (1999).

Meyer, J.

S. M. Sadeghi, S. R. Leffler, and J. Meyer, “Quantum interference and nonlinear optical processes in the conduction bands of infrared-coupled quantum wells,” Phys. Rev. B 59, 15388–15394 (1999).

Müller, T.

T. Müller, W. Parz, G. Strasser, and K. Unterrainer, “Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well,” Phys. Rev. B 70, 155324(1–5) (2004).

Nakajima, T.

T. Nakajima and S. Watanabe, “Effects of the carrier-encelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96, 213001(1–4) (2006).

T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31, 1920–1922 (2006).
[PubMed]

Parz, W.

T. Müller, W. Parz, G. Strasser, and K. Unterrainer, “Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well,” Phys. Rev. B 70, 155324(1–5) (2004).

Paspalakis, E.

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semicondutor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).

G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000).
[PubMed]

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency of a short laser pulse via decay interference in a closed V-type system,” Phys. Rev. A 61, 045802(1–4) (1999).

Pfeiffer, L. N.

J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).

Phillips, C. C.

M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).

G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000).
[PubMed]

Ploog, K. H.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Pronin, K. A.

K. A. Pronin and A. D. Bandrauk, “Coherent Control of Harmonic Generation in Superlattices: Single-Mode Response,” Phys. Rev. Lett. 97, 020602(1–4) (2006).

Reimann, K.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Roos, P. A.

T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

Sadeghi, S. M.

S. M. Sadeghi, S. R. Leffler, and J. Meyer, “Quantum interference and nonlinear optical processes in the conduction bands of infrared-coupled quantum wells,” Phys. Rev. B 59, 15388–15394 (1999).

Schmidt, H.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoğlu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).

H. Schmidt and A. Imamoglu, “Nonlinear optical devices based on a transparency in semiconductor intersubband transitions,” Opt. Commun. 131, 333–338 (1996).

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).

Serapiglia, G. B.

G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000).
[PubMed]

Silvestri, L.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).

Sipe, J. E.

T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

Sirtori, C.

G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000).
[PubMed]

J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).

J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

Song, X.

C. Zhang, X. Song, W. Yang, and Z. Xu, “Carrier-envelope phase control of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well,” Opt. Express 16, 11487–1496 (2008).

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).

Strasser, G.

T. Müller, W. Parz, G. Strasser, and K. Unterrainer, “Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well,” Phys. Rev. B 70, 155324(1–5) (2004).

Swain, S.

Z. Ficek and S. Swain, Quantum Interference and Coherence (Springer, New York, 2004).

Terzis, A. F.

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semicondutor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).

Tsaousidou, M.

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semicondutor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).

Unterrainer, K.

T. Müller, W. Parz, G. Strasser, and K. Unterrainer, “Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well,” Phys. Rev. B 70, 155324(1–5) (2004).

Van Vlack, C.

C. Van Vlack and S. Hughes, “Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors,” Phys. Rev. Lett. 98, 167404(1–4) (2007).

Vodopyanov, K. L.

G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000).
[PubMed]

Waldmüller, I.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Watanabe, S.

T. Nakajima and S. Watanabe, “Effects of the carrier-encelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96, 213001(1–4) (2006).

T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31, 1920–1922 (2006).
[PubMed]

West, K. W.

J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).

J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

Williams, B. S.

B. S. Williams, B. Xu, Q. Hu, and M. R. Melloch, “Narrow-linewidth terahertz intersubband emission from three-level systems,” Appl. Phys. Lett. 75, 2927–2929 (1999).

Woerner, M.

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

Wu, J. H.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

Wu, Y.

Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76, 013832(1–4) (2007).

Y. Wu and X. Yang, “Strong-Coupling Theory of Periodically Driven Two-Level Systems,” Phys. Rev. Lett. 98, 013601(1–4) (2007).

Xu, B.

B. S. Williams, B. Xu, Q. Hu, and M. R. Melloch, “Narrow-linewidth terahertz intersubband emission from three-level systems,” Appl. Phys. Lett. 75, 2927–2929 (1999).

Xu, J. H.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

Xu, Z.

C. Zhang, X. Song, W. Yang, and Z. Xu, “Carrier-envelope phase control of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well,” Opt. Express 16, 11487–1496 (2008).

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).

Yang, W.

C. Zhang, X. Song, W. Yang, and Z. Xu, “Carrier-envelope phase control of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well,” Opt. Express 16, 11487–1496 (2008).

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).

Yang, W. X.

W. X. Yang and R.-K. Lee, “Controllable entanglement and polarization phase gate in coupled double quantum-well structures,” Opt. Express 16, 17161–17170 (2008).
[PubMed]

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).

Yang, X.

Y. Wu and X. Yang, “Strong-Coupling Theory of Periodically Driven Two-Level Systems,” Phys. Rev. Lett. 98, 013601(1–4) (2007).

Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76, 013832(1–4) (2007).

Zhang, C.

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).

Appl. Phys. Lett. (3)

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoğlu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).

B. S. Williams, B. Xu, Q. Hu, and M. R. Melloch, “Narrow-linewidth terahertz intersubband emission from three-level systems,” Appl. Phys. Lett. 75, 2927–2929 (1999).

J. Faist, F. Capasso, C. Sirtori, A. L. Hutchinson, K. W. West, and L. N. Pfeiffer, “Itersubband emission in double-well structure with quantum interference in absorption,” Appl. Phys. Lett. 71, 3477–3479 (1997).

Eur. Phys. J. B (1)

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).

Nature (London) (1)

J. Faist, F. Capasso, C. Sirtori, K. W. West, and L. N. Pfeiffer, “Controlling the sign of quantum interference by tunnelling from quantum wells,” Nature (London) 390, 589–591 (1997).

Nature Materials (1)

M. D. Frogley, J. F. Dynes, M. Beck, J. Faist, and C. C. Phillips, “Gain without inversion in semiconductor nanostructures,” Nature Materials 5, 175–178 (2006).

Opt. Commun. (1)

H. Schmidt and A. Imamoglu, “Nonlinear optical devices based on a transparency in semiconductor intersubband transitions,” Opt. Commun. 131, 333–338 (1996).

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (3)

Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76, 013832(1–4) (2007).

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency of a short laser pulse via decay interference in a closed V-type system,” Phys. Rev. A 61, 045802(1–4) (1999).

Phys. Rev. B (5)

D. Ahn and S. L. Chuang, “Exact calculations of quasibound states of an isolated quantum well with uniform electric field: Quantum-well stark resonance,” Phys. Rev. B 34, 9034–9037 (2008).

I. Waldmüller, J. Förstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semicondutor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).

T. Müller, W. Parz, G. Strasser, and K. Unterrainer, “Influence of carrier-carrier interaction on time-dependent intersubband absorption in a semiconductor quantum well,” Phys. Rev. B 70, 155324(1–5) (2004).

S. M. Sadeghi, S. R. Leffler, and J. Meyer, “Quantum interference and nonlinear optical processes in the conduction bands of infrared-coupled quantum wells,” Phys. Rev. B 59, 15388–15394 (1999).

Phys. Rev. Lett. (11)

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark Splitting and Quantum Interference with Intersubband Transitions in Quantum Wells,” Phys. Rev. Lett. 94, 157403(1–4) (2005).

G. B. Serapiglia, E. Paspalakis, C. Sirtori, K. L. Vodopyanov, and C. C. Phillips, “Laser-induced quantum coherence in a semiconductor quantum well,” Phys. Rev. Lett. 84, 1019–1021 (2000).
[PubMed]

Y. Wu and X. Yang, “Strong-Coupling Theory of Periodically Driven Two-Level Systems,” Phys. Rev. Lett. 98, 013601(1–4) (2007).

G. L. Kamta and A. D. Bandrauk, “Phase Dependence of Enhanced Ionization in Asymmetric Molecules,” Phys. Rev. Lett. 94, 203003(1–4) (2005).

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-Envelope Phase Dependence of Few-Cycle Ultrashort Laser Pulse Propagation in a Polar Molecule Medium,” Phys. Rev. Lett. 99, 133602(1–4) (2007).

T. M. Frontier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, “Carrier-Envelope Phase-Controlled Quantum Interference of Injected Photocurrents in Semiconductors,” Phys. Rev. Lett. 92, 147403(1–4) (2004).

K. A. Pronin and A. D. Bandrauk, “Coherent Control of Harmonic Generation in Superlattices: Single-Mode Response,” Phys. Rev. Lett. 97, 020602(1–4) (2006).

C. Van Vlack and S. Hughes, “Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors,” Phys. Rev. Lett. 98, 167404(1–4) (2007).

T. Nakajima and S. Watanabe, “Effects of the carrier-encelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96, 213001(1–4) (2006).

E. Paspalakis, N. J. Kylstrra, and P. L. Knight, “Transparency induced via decay interference,” Phys. Rev. Lett. 82, 2079–2082 (1999).

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).

Other (3)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).

Z. Ficek and S. Swain, Quantum Interference and Coherence (Springer, New York, 2004).

H.C. Liu and F. Capasso, Intersubband Transitions in Quantum Wells: Physics and Device Applications (Academic Press, San Diego, 2000).

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Figures (3)

Fig. 1.
Fig. 1. (a) Schematic diagram of our proposed GaAs/AlxGa1-xAs QW structure illuminated by an ultrashort few-cycle laser pulse in (b), where the electric field E(t) of the ultrashort pulse versus time t is shown for ϕ=π/2.
Fig. 2.
Fig. 2. The transient coherence ρ 23×104 versus the CEP, ϕ, (solid curves for the real part; dashed curves for the imaginary part; and dotted curves for the absolute value, respectively) at the time t=4τ for different widths, τ, and Rabi frequencies, Ω, of the pulse with other parameters h̄ω=125 meV, q=1.2, Δ=0, 2δ=7.6 meV, γ2l =5.6 meV, γ3l =7.0 meV, γ2d =4.13 meV, and γ3d =5.35 meV.
Fig. 3.
Fig. 3. The transient coherence |ρ 23|×104 versus the CEP ϕ for the case of (a, c) p=0 and (b, d) p=1 at the time t=4τ for different widths, τ, and Rabi frequencies, Ω, of the pulse with other parameters h̄ω=125 meV, q=1.2, Δ=0, 2δ=17.6 meV, γ2l =0.31 meV, γ3l =0.26 meV, γ2d =0.031 meV, and γ3d =0.026 meV.

Equations (7)

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a.1 = i Ω ξ (t)[a2(t)eiΔt+qa3ei(Δ+δ)t],
a.2 = γ2 a2 + i Ω ξ (t)a1eiΔt+pγ2γ3a3eiδt,
a.3 = γ3 γ3 + i Ω ξ (t)qa1ei(Δ+δ)t + p γ2γ3 a2 eiδt ,
I = ψ(T)Ê1()(T)Ê2(+)(T)ψ(T)+c.c.,
i(ddT+γj)ajpγ2γ3(a3δj,2+a2δj,3)=gjbj,
i dbjdT gj aj = 0,j=2,3,
I = I0 (ϕ)cos[2δ(Tt)+η(t)],

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