Open Access
Add to BibSonomyAbstract
We present a coherent multi-frequency source generated from a mode-locked femto-second laser. The key concept for the coherent multi-frequency source generation is using the mode-locked femto-second laser as many continuous wave (CW) optical sources. We simultaneously selected and amplified the desired modes of the optical frequency comb using femtosecond laser injection-locking (FSLIL). Using two coherent sources generated by the mode-locked femto-second laser, we have demonstrated a coherent spectroscopy in a A-type system of the Cs D2 line. The proposed coherent multi-frequency source generation technique will be a useful technique for optical frequency standards based on multi-photon schemes.
©2007 Optical Society of America
1. Introduction
A mode-locked femto-second laser is a pulse laser with a femto-second pulse-width in the time space and an optical frequency comb (OFC) which is used as a precise ruler in the frequency space [1–6]. Since the optical frequency is measured absolutely using the OFC, it focuses on the frequency accuracy of the mode spacing of the OFC. However, in the frequency space, the mode-locked femto-second laser is also considered as many continuous wave (CW) optical sources. The CW optical sources from the OFC are not only uniform in frequency space, but also coherent with one another. If the modes of the OFC are used as the CW laser sources, a coherent multi-frequency source with stable frequencies and narrow linewidth is obtained.
Coherent multi-frequency sources are important for frequency references in the optical frequency region [7–9]. Recently, the optical frequency standard has been actively studied using even isotopes of alkaline earth-like atoms in the optical lattices, because the nonzero nuclear spin of the odd isotopes creates undesirable residual lattice polarization sensitivity, optical pumping issues, and linear magnetic field sensitivity [7–11]. However, the excitation of the doubly forbidden intercombination transition (clock transition) in the even isotopes is forbidden due to the absence of hyperfine mixing.
Fig. 1. Multi-photon schemes for the doubly forbidden intercombination transition in the even isotopes of alkaline earth-like atoms; (a) three-level system [8], and (b) four-level system [7].
One of the approaches used to resolve this problem is the direct optical excitation of the transition in the even isotopes by adding a small magnetic field to mix a fraction of a nearby state into the upper clock state, creating a weak electric dipole transition [10–11]. Another approach is the use of multi-photon schemes [7–9], as shown in Fig. 1. Figure 1(a) is a three-level atomic system for an optical lattice clock presented by R. Santra et al. [8] and Fig. 1(b) is a four-level atomic system introduced by T. Hong et al. [7]. In order to realize such multi-photon schemes, it is essential that multiple lasers are phase coherent with each other. For multi-photon schemes, the frequency differences among multiple lasers are too large, from several THz to hundreds of THz, and they cannot use well-known phase locking techniques such as electrical or optical methods. Therefore, R. Santra et al. proposed difference frequency generation using a nonlinear optical crystal in order to implement their scheme [8]. However, the proposed method for the realization of the multi-photon schemes is relatively difficult and complex resulting from the use of multiple stabilized lasers and nonlinear optics [10].
In this paper, we propose a coherent multi-frequency source generation technique that can realize such multi-photon schemes. The key concept of the coherent multi-frequency source generation technique is to select the desired frequency components from the optical frequency comb simultaneously. Recently, we developed a femto-second laser injection-locking (FSLIL) technique to select and amplify the desired component of an OFC [12–13]. The FSLIL technique involves the selection and amplification of the desired component of an optical frequency comb (OFC) using a mode-locked Ti:sapphire laser as the master laser and a single-mode diode laser as the slave laser. If the FSLIL technique is simultaneously applied to two more single-mode lasers with different frequencies, our proposed method can be relatively simple for experimental implementation of the multi-photon schemes.
In this paper, we applied the FSLIL technique to two distributed Bragg reflector (DBR) lasers in order to generate a coherent multi-frequency source. When the two modes are selected from one OFC, the two DBR lasers are phase coherent with each other because the characteristics of the two injection-locked slave lasers follow those of the only master laser. Using two coherent sources generated from the OFC, we have demonstrated the coherent spectroscopy in a Cs D2 line. We propose an optical frequency standard based on coherent population trapping (CPT) in applications such as CPT clocks in the radio frequency region.
2. Experimental setup
Figure 2 is the experimental setup used to generate the coherent multi-frequency source and demonstrate a coherent spectroscopy. In our experiment, we used a mode-locked Ti:sapphire laser with a repetition rate of 1.05 GHz as the master laser. The mode-locked Ti:sapphire laser pulse-width was approximately 50 fs and the center wavelength was 820 nm with a 30 nm spectral width. The average power was approximately 550 mW, pumped by single-mode 5.5 W solid-state laser at 532 nm. The repetition rate frequency (f rep) was stabilized to an H-maser. Although the carrier-envelope-offset frequency (f ceo) can be stabilized by employing an f-to-2f interferometer [13], the f ceo was not stabilized for this experiment. The two DBR lasers used as the slave lasers were single-mode operated diodes at 852 nm near the Cs D2 line. The output powers of the two DBR lasers are 150 mW, but the DBR lasers were used at around 50 mW for this experiment.
Fig. 2. Experimental setup for the generation of the coherent multi-frequency source and the coherent spectroscopy in a Cs D2 line (DBR: distributed Bragg reflector diode laser, F: 852 nm interference filter, FR: Faraday rotator, AOM: acoustic optic modulator, M: mirror, LP: linear polarizer, AP: aperture, PBS: polarizing beam splitter, BS: beam splitter, PD: Si photodiode).
The output of the mode-locked Ti:sapphire laser was divided into two paths using a pellicle beam splitter. The laser reflected from the pellicle beam splitter was used for optical injection-locking and the power was approximately 45 mW. We used an interference filter, with a center wavelength of 852 nm and a transmittance bandwidth of 1.5 nm, to select the near wavelength of the slave laser and to prevent optical damage in the slave laser which may result from the injection of the femto-second laser. After passing through the interference filter, the total power of the OFC was approximately 160 μ W and the number of transmitted modes was approximately 600. The power per mode was estimated to be approximately 260 nW.
In order to simultaneously inject the master laser into the two slave lasers, the laser passed through a half-wave plate (HWP; λ/2 plate) and was divided by a beam splitter with 50% transmittance. The optical power injected into each DBR laser was less than 130 nW. Because the power per mode of the OFC is low, the injected optical power needs to be maintained and this was accomplished by using two polarization beam splitters (PBS) and a Faraday rotator for injection-locking for each DBR laser. The saturated absorption spectroscopy in each DBR laser was installed to monitor the injection-locking characteristics.
In order to obtain CPT spectrum in a Cs D2 line using the two injection-locked DBR lasers, two coherent laser beams, DBR1 and DBR2, co-propagated through the Cs vapor cell. We controlled each laser’s power with a HWP and overlapped the two laser beams with a polarizing beam splitter (PBS). After overlapping, the two laser beams were circularly polarized using a quarter-wave plate (QWP; λ/4 plate). We then directed the beams to pass through an aperture with a 2 mm diameter and a Cs vapor cell. The 2.5 cm diameter, 2.5 cm long Cs vapor cell contained a neon buffer gas at 20 Torr. In order to minimize the effect of the earth’s magnetic field, we wrapped the Cs cell with a μ-metal sheet twice. A 150 mm solenoid was used to ensure the homogeneity of the magnetic field inside the cell in order to separate the Zeeman sublevels. The two laser beams were detected using a Si photodiode (PD1).
3. Experimental results and discussions
Figure 3 shows the energy level diagram for CPT in a Λ-type system of a Cs D2 line. In order to obtain the CPT spectrum, the frequency difference between the two coherent lasers should be equal to the hyperfine frequency between the ground states. Tuning the frequencies of the free-running DBR lasers, we injected the two different desired modes of the OFC into the two DBR lasers. By monitoring the saturated absorption spectrum (SAS) of each DBR laser, we can select the two modes of OFC near the F=3 → F’=4 and the F=4 → F’=4 transitions by adjusting the currents of the DBR lasers. When the DBR laser was optically injection-locked by the OFC, we found that the SAS remained unchanged by the frequency of the slave laser, as shown by the SAS in Fig. 4. This is because each slave laser was locked to each single component of the OFC. In this time, the power injected into each slave laser was 30 μW and the locking range was approximately 60 MHz. The SAS of DBR1 is shown in Fig. 4(a). In this case, we can see that the SAS plate is near the F=4 → F’=3 transition, as shown by the circular dot in Fig. 4(a). The frequency of DBR1 was locked to the mode of the OFC near the F=4 → F’=3 transition. For DBR2, the SAS of DBR2 is the plate in the F=4 → F’=4 transition, as shown by the circular dot in Fig. 4(b).
Fig. 3. The energy level diagram of the 6S1/2-6P3/2 transition of a Cs atom: CPT is accomplished using the two laser fields applied in a Λ-type scheme (Ωb: probe laser and ΩC: coupling laser).
Fig. 4. Saturated absorption spectrum (SAS) of a Cs D2 line optically injection-locked by OFC; (a) injection-locking near the F=4 → F’=3 transition, and (b) injection-locking in the F=4 → F’=4 transition.
In order to obtain the CPT spectrum in the atomic system of Fig. 3, the frequency difference between the two coherent lasers should be equal to the hyperfine frequency of 9.2 GHz between the ground states; however, the frequency between the two selected modes of the OFC is not equal to the hyperfine frequency between the ground states. That is, the integral times (n) of the repetition rate (f rep) of the mode-locked Ti:sapphire laser used (n × 1.05 GHz) is not 9.2 GHz, the frequency difference between the F=3 and F=4 ground states. In order to adjust the frequency difference between the two coherent sources to the hyperfine frequency (f hyp) between the ground states, we used an acoustic optic modulator (AOM) with a 114 MHz resonance (f AOM). As shown by the experimental setup in Fig. 2, the beam of DBR1 passed though the AOM twice. After passing through the AOM, the frequency of the DBR1 shifted to 228 MHz in the F=4 → F’=3 transition, as shown by the arrow in Fig. 4(a). Therefore, the frequency difference between the two selected modes of the OFC was satisfied with this relation, f hyp= n×f rep - 2×f AOM, as shown by the SAS in Fig. 4. In this experiment, another function of the AOM is frequency scanning in order to observe the CPT spectrum.
Fig. 5. The Λ-type CPT spectrum of the 6S1/2-6P3/2 transition of Cs. The linewidth of the CPT spectrum is 1.4 kHz and the contrast is approximately 1%.
Figure 5 shows the CPT spectrum of the 6S1/2 – 6P3/2 transition of Cs using the multi-frequency source generated from the OFC, where the horizontal axis of the figure is detuning from the resonance between the two ground states in the 6S1/2 state of Cs. This CPT spectrum is due to couple the ground states ∣6S 1/2;F = 3;mF = 0〉 and ∣6S 1/2;F = 4;mF = 0〉 to a common level of the 6P3/2 excited state. The frequency of the AOM was scanned in the region near the resonance between the two ground states where the laser intensity was 15 μW/cm2. In Fig. 5, the linewidth of the CPT spectrum is 1.4 kHz and the contrast is approximately 1%. The CPT linewidth is related to the laser power, transient broadening, relative phase noise between the two lasers, and the relaxation rates. The contrast is defined as the CPT signal intensity divided by the background intensity. Although all the experimental conditions are not completely optimized for a narrow CPT spectrum, the observed CPT spectrum is enough to show the two coherent sources generated from the OFC. The asymmetrical resonance line in Fig. 5 is a result of the temporal evolution effect of the CPT by the frequency scanning of the probe laser.
In this experiment, we observed the CPT spectrum by scanning the driving frequency of the AOM. However, it is possible to obtain the CPT signal by scanning the repetition rate of the OFC instead of the driving frequency of the AOM. However, changing the repetition rate of the OFC and observing the CPT in the atomic system of Fig. 3, because the frequency shift of 10 kHz in the 9.2 GHz RF region leads to 380 MHz in the 352 THz optical region, the CPT spectrum is distorted due to the Doppler profile of linear absorption. Furthermore, the modes of the OFC are not in the desired injection-locking bandwidth. But, if the frequency difference between the ground states is large enough, we can obtain the CPT signal by scanning the mode spacing of the OFC and locking the mode spacing of the OFC into the CPT signal. This means that the repetition rate of the optical comb can be locked to the CPT spectrum.
If the repetition rate of the optical comb is locked to the CPT, it is possible to develop optical frequency standards based on coherent population trapping (CPT) such as CPT clocks in the radio frequency region. For an optical coherent population trapping (OCPT) clock, the OCPT spectrum is generated using the multi-frequency source from the OFC, and the repetition rate of the optical comb is locked to the optical CPT spectrum in a multi-photon scheme [8–9]. Due to the large frequency difference between the two coherent radiations in the optical frequency region, we cannot eliminate the Doppler Effect in an atomic vapor cell. It is necessary that the trapped alkaline earth-like atom has a meta-stable state, such as Ca, Sr, or Yb, in order to obtain the CPT signal in the optical frequency region [7–9].
4. Conclusion
We generated a coherent multi-frequency source using a FSLIL and demonstrated the coherent spectroscopy in a Cs D2 line. In order to generate a coherent multi-frequency source, we applied the FSLIL technique to two distributed Bragg reflector (DBR) lasers. The mode-locked Ti:sapphire laser with a repetition rate of 1.05 GHz was used as a master laser, and two DBR lasers with a single-mode diode operated at 852 nm near the Cs D2 line were used as slave lasers. When the two modes were selected from one OFC, the two DBR lasers were phase coherent with each other because the characteristics of the two injection-locked slave lasers follow those of the master laser. We observed the CPT spectrum of the 6S1/2 – 6P3/2 transition of Cs using the multi-frequency source generated from the OFC. The linewidth of the CPT spectrum was 1.4 kHz and the contrast was approximately 1%. If the mode spacing of the OFC can be locked into the CPT signal, the repetition rate of the mode-locked femto-second laser can be locked into a CPT clock instead of an H-maser. We believe that our results will prove to be a useful technique in optical frequency standards based on the multi-photon schemes [7–9] and optical CPT clocks, such as CPT clock in radio frequency region.
References and links
1. Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the Cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82,3568–3571 (1999). [CrossRef]
2. J. Reichert, M. Niering, R. Holzwarth, M. Weitz, Th. Udem, and T. W. Hänsch, “Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser,” Phys. Rev. Lett. 84,3232–3235 (2000). [CrossRef] [PubMed]
3. D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288,635–639 (2000). [CrossRef] [PubMed]
4. Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416,233–237 (2002). [CrossRef] [PubMed]
5. S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75,325–342 (2003). [CrossRef]
6. M. Takamoto, F. Hong, R. Higashi1, and H. Katori, “An optical lattice clock,” Nature 435,321–324 (2005). [CrossRef] [PubMed]
7. T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94, 050801 (2005). [CrossRef] [PubMed]
8. R. Santra, E. Arimondo, T. Ido, C. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic 88Sr,” Phys. Rev. Lett. 94, 173002 (2005). [PubMed]
9. T. Zanon-Willette, A. Ludlow, S. Blatt, M. Boyd, E. Arimondo, and J. Ye, “Cancellation of Stark shifts in optical lattice clocks by use of pulsed raman and electromagnetically induced transparency techniques,” Phys. Rev. Lett. 97, 233001 (2006). [CrossRef]
10. A. V. Taichenachev, V. I. Yudin, C. W. Oates, C. W. Hoyt, Z. W. Barber, and L. Hollberg, “Magnetic field-induced spectroscopy of forbidden optical transitions with application to lattice-based optical atomic clocks,” Phys. Rev. Lett. 96, 083001 (2006). [CrossRef] [PubMed]
11. Z. W. Barber, C. W. Hoyt, C. W. Oates, L. Hollberg, A. V. Taichenachev, and V. I. Yudin, “Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice,” Phys. Rev. Lett. 96, 083002 (2006). [CrossRef] [PubMed]
12. H. S. Moon, E. B. Kim, S. E. Park, and C. Y. Park, “Selection and amplification of modes of an optical frequency comb using a femtosecond laser injection-locking technique,” Appl. Phys. Lett. 89, 181110 (2006). [CrossRef]
13. S. E. Park, E. B. Kim, Y.-H. Park, D. S. Yee, T. Y. Kwon, C. Y. Park, H. S. Moon, and T. H. Yoon, “Sweep optical frequency synthesizer with a distributed-Bragg-reflector laser injection locked by a single component of an optical frequency comb,” Opt. Lett. 31,3594–3596 (2006). [CrossRef] [PubMed]
