On-chip low loss heralded source of pure single photons

Justin B. Spring; Patrick S. Salter; Benjamin J. Metcalf; Peter C. Humphreys; Merritt Moore; Nicholas Thomas-Peter; Marco Barbieri; Xian-Min Jin; Nathan K. Langford; W. Steven Kolthammer; Martin J. Booth; Ian A. Walmsley

doi:10.1364/OE.21.013522

1. Introduction

Photonic quantum-enhanced technologies aim to employ nonclassical states of light to surpass classical performance limits in diverse fields including computation [1, 2], metrology [3], and communication [4]. An impediment to faster progress is the quality of available single photon sources. Building the low-loss sources of high purity single photons necessary for quantum-enhanced performance has proven challenging [5–9].

Heralding spontaneous emission from a nonlinear-optical material has to date been the most common method of generating single photons [10–13]. Nonlinear processes such as spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM) can be used to create pairs of photons. Due to this pairwise emission, detection of one photon, the heralding photon, indicates the creation of its partner, the heralded single photon. A key source metric is the preparation efficiency η_P, the conditional probability that a heralded photon is delivered to its application given detection of the heralding photon. For example, the rate at which multiphoton states are generated from single-photon sources scales exponentially with η_P, even with multiplexing strategies which ideally achieve near-deterministic emission [14]. In numerous applications, η_P is a crucial parameter for a quantum method to demonstrate true advantage over a classical approach [6–9].

Four-wave mixing in a silica waveguide is a promising route to achieving exceptionally high η_P[12, 15]. In heralded photon sources, reduction in η_P results from loss of the heralded photon, due to scattering or imperfect mode-matching at interfaces. Waveguides in commonly available silica glasses minimize these effects due to their exceedingly low optical loss and excellent mode-matching to optical fiber, a ubiquitous component in quantum photonics. While silica’s relatively small χ⁽³⁾ nonlinearity affects the emitted photon flux, in many applications it is loss that is fundamental to demonstrating quantum enhancement, not flux. In fact, for heralded single photon sources one must deliberately keep emission rates low to avoid unwanted heralding of more than one photon. The transverse confinement of the waveguide allows these desired photon production rates to be reached at readily available pump powers.

Typical quantum applications require heralded photons in pure quantum states in addition to high source η_P. In general, however, the heralded pair source generates mixed quantum states. Energy and momentum conservation can lead to entanglement between multiple spatial and spectral modes of the emitted photon pairs [16, 17]. If the heralding photon is detected but its mode is not resolved, then the heralded photon is left in a mixed quantum state of all possible modes. One approach to achieve a high-purity heralded photon is to use spectral and spatial filters on the heralding field which ensures the detector responds to only a single spatio-temporal mode. Such filters reduce the rate at which heralded photons are emitted. On-chip SPDC sources are capable of high photon flux [18–21] that allows acceptable count rates even when filters are used to achieve good photon purity. For SFWM in silica, on the other hand, the reduced count rate from this approach could lead to unacceptably long data collection times.

An alternate approach we employ here is to engineer the source to emit photons into a single pair of modes. As a consequence, the heralding and heralded photon are not entangled. The resulting factorable output allows heralded photons of high purity without filtering. Guided-wave photonics allows the precise control of optical modes needed to construct such a source. Previous silica sources have demonstrated this strategy using optical fibers. In these structures, however, fabrication inhomogeneity [11, 22] or sensitivity to the local environment [12, 23–25] prevented a robust scalable solution. While on-chip SFWM sources have been demonstrated in chalcogenide glass [26] and silicon [27], these devices exhibited relatively high loss and did not pursue the factorable source design strategy described here.

Here we report the first photon source on a silica photonic chip. Our SFWM source generates heralded single photons of purity P = 0.86 and η_P = 80% without narrow spectral filtering. Heralded single photons are emitted at a rate of 3.1 · 10⁵ photons per second with a pump field power of 150 mW. We use a birefringent waveguide to phasematch SFWM at frequencies where the reddetuned photon lies far beyond silica’s Raman gain peak. This minimizes spontaneous Raman scattering [12, 15, 28], which is the principal noise source in many silica sources [29, 30]. A solid-clad silica waveguide provides a convenient and robust platform for our source which we foresee finding immediate application in integrated quantum optics experiments that frequently rely on similar integrated silica architectures [2, 13, 31–35].

2. Experimental overview

Our source uses a 4 cm long waveguide fabricated by femtosecond laser writing in an undoped silica chip (Lithosil Q1) [36, 37]. We use adaptive optics to shape the writing beam [38] and produce an elliptical transverse mode yielding a birefringence of Δn = 10⁻⁴.

A single pump field with central wavelength λ_p = 729 nm is generated by an 80 MHz Ti-Sapphire oscillator whose spectral bandwidth Δλ_p is adjusted with a mechanical slit in a 4-f line, as shown in Fig. 1(a). We describe the high (low) frequency photon in the emitted pair as the signal (idler). A dichroic beam splitter (Semrock FF740) separates these signal and idler photons which have central wavelengths of λ_s = 676 and λ_i = 790 nm. A combination of spectral (Semrock 684/24 and 800/12) and polarization filters extinguish the pump field before the signal and idler modes are coupled into single-mode fibers. Silicon avalanche photodiodes (APDs) (Perkin Elmer SPCM-AQ4C) and an FPGA-based coincidence counter (Xilinx SP-605) are used to measure marginal and joint photon statistics as shown in Figs. 1(b)–1(d) and discussed below.

Fig. 1 The experimental layout consists of (a) state preparation and (b–d) characterization. (a) A 4-f line with an adjustable slit is used to control the bandwidth of the pump (Δλ_p). After the chip, the pump is filtered out while the signal and idler fields are separated by a dichroic mirror (DM) and coupled into separate single-mode fibers (SMFs). (b) Source count rate and cross-correlation $g_{si}^{(2)} (0)$ are measured with the SMFs coupled directly into avalanche photodiodes (APDs). (c) The autocorrelation $g_{ii}^{(2)} (0)$ is measured by connecting the idler fiber to a fiber beam splitter (BS) with a reflectivity of 50% and ignoring the signal field, while the signal field is used as a herald when determining $g_{H}^{(2)} (0)$ . We measure $g_{ss}^{(2)} (0)$ by inserting the signal fiber into the BS and ignoring the idler field (not shown). (d) To measure joint spectral intensities, the source SMFs are connected to separate monochromators with multi-mode fibers (MMFs) at the output performing a raster scan over the joint spectral range while APDs count in coincidence.

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3. Nonclassical emission and heralding of single photons

We first confirm nonclassical operation of our source by measuring the cross- and autocorrelations of the signal and idler modes with the setup shown in Figs. 1(b) and 1(c). Classical fields must satisfy the Cauchy-Schwarz inequality ${(g_{si}^{(2)} (0))}^{2} \leq g_{ss}^{(2)} (0) \cdot g_{ii}^{(2)} (0)$ where $g_{x y}^{(2)} (τ)$ is the second order coherence between modes x and y at relative time delay τ[39]. For our pulsed source, we calculate

g_{x y}^{(2)} (0) = \frac{N_{x y} N_{p}}{N_{x} N_{y}}

where N_x (N_xy) correspond to single (temporally coincident) detection events on mode x (x and y). The number of trials is given by N_p, the number of pulses from the Ti-Sapphire pump. Autocorrelations are described by

g_{x_{1} x_{2}}^{(2)} (0)

where x_1,2 refer to the two output ports of a fiber beam splitter with a reflectivity of 50% as shown in Fig. 1(c). For brevity, we write autocorrelations as

g_{x x}^{(2)} (0)

where the use of two output modes of a beam splitter is implied.

With the pump bandwidth Δλ_p = 3.1 nm and 100 mW average power, we measure $g_{si}^{(2)} (0) = 73.5 \pm 1.1$ , $g_{ss}^{(2)} (0) = 1.82 \pm 0.03$ , and $g_{ii}^{(2)} (0) = 1.26 \pm 0.02$ with no background subtraction. The Cauchy-Schwarz inequality is violated here by 49 standard deviations which demonstrates a nonclassical correlation between signal and idler modes in the photon number basis.

It is this correlation in photon number that makes such sources suitable for heralding single photons. Using the signal photon as the heralding photon, we measure the heralding efficiency η_H = N_si/N_s. We calculate η_H > 40% for pump powers of 75 to 150 mW as seen in Fig. 2. The measured η_H is limited primarily by the detector efficiency, which can be readily improved [40]. We thus estimate the preparation efficiency η_P, which corresponds to the probability that the idler photon arrives at its detector given detection of the heralding signal photon. Due to the difficulty of precisely measuring absolute detector efficiencies, we follow the practice [12, 21] of using the manufacturer’s specifications which results in an estimated η_p = 80% for our source. The remaining inefficiency is due to loss in the heralded idler mode estimated as follows: coupling into an un-coated single mode fiber, including interface reflections and spatial mode mismatch (10% total loss); reflection at the uncoated chip interface (3% loss); spectral filters that achieve over 100 dB extinction of the pump (1.5% loss); and propagation loss in the chip. The similar losses that occur in the signal mode do not affect η_p.

Fig. 2 The count rate for the signal mode alone (N_s) and in temporal coincidence with the idler mode (N_si) is shown as a function of the pump power (blue circles). The heralding efficiency, which includes APD detector losses, is calculated according to η_H = N_si/N_s (green). At low pump powers, η_H decreases due to the heightened importance of detector dark counts, which cause false herald events. The heralded autocorrelation of the idler photon with the signal field as herald, $g_{H}^{(2)} (0)$ , increases linearly due to spontaneous Raman scattering (red squares). Quadratic (blue) and linear (red) fits to the data are shown with dotted lines. Error bars are smaller than the markers for the count data and $g_{H}^{(2)} (0)$ .

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We quantify the suppression of undesired higher order photon emission by measuring $g_{H}^{(2)} (0)$ , the heralded second-order coherence of the idler mode, using the apparatus shown in Fig. 1(c). We calculate

g_{H}^{(2)} (0) = \frac{N_{i_{1} i_{2} s} N_{s}}{N_{i_{1} s} N_{i_{2} s}}

where the number of two- and three-fold coincident detection events between the signal and the two arms of the idler after the beam splitter are given by N_i₁s,N_i₂s, and N_i₁i₂s. An ideal single-photon source would give

g_{H}^{(2)} (0) = 0

. We measure

g_{H}^{(2)} (0) = 0.0092 \pm 0.0004

for a pump power of 25 mW. Spontaneous Raman scattering is the primary noise source, which explains the linear increase in

g_{H}^{(2)} (0)

as the source is pumped harder. Our low

g_{H}^{(2)} (0)

values are comparable to other SFWM sources [15, 25] that take advantage of birefringent phase matching [28], which allows significant suppression of this Raman noise which has inhibited other SFWM sources [29, 30].

4. Controlling the heralded state purity

The pairwise emission that allows heralding of single photons is not sufficient for many applications; these photons must also be in pure states. Undesired correlations between the signal and idler fields that are not resolved by the heralding detector instead result in heralding of mixed states. Such correlations imply multimode emission in the frequency, polarization, or spatial degrees of freedom. Phasematching constraints generally force the signal and idler fields to be emitted into single polarizations. Furthermore, our waveguide constrains each of the three fields (pump, signal, idler) to a single spatial mode. This is more readily achieved for a SFWM source, in contrast to SPDC, due to the reduced disparity in field frequencies.

We focus on the remaining possibility that correlations are generated in the spectral degree of freedom. The effective SFWM Hamiltonian can thus be approximated as [16]

{\hat{H}}_{SFWM} = ζ \iint d ω_{s} d ω_{i} f (ω_{s}, ω_{i}) {\hat{a}}^{†} (ω_{s}) {\hat{b}}^{†} (ω_{i}) + H . c .

where the joint spectral amplitude f(ω_s, ω_i)= ∫ dω′α(ω′)α(ω_s+ω_i−ω′)ϕ(ω_s, ω_i) is a function of the pump envelope α(ω) and phasematching function ϕ(ω_s, ω_i), while ζ depends on both the pump intensity and magnitude of the χ⁽³⁾ nonlinearity. We approximate α(ω) as a Gaussian function and specify Δλ_p as the full-width at half maximum of |α(ω)|². The phase-matching function results from integrating over the length of the guide

ϕ (ω_{s}, ω_{i}) = \int_{0}^{L} e^{i Δ k z} d z \propto e^{i Δ k L} sinc (Δ k L / 2)

, where the wavevector mismatch is Δk = 2k_p − k_s − k_i. We neglect the phase mismatch arising from the pump pulse intensity, since this is small for our source. In the normal dispersion regime, SFWM is phase-matched (Δk = 0) when the pump field is polarized along the slow axis and both signal and idler fields are polarized along the fast axis of the birefringent waveguide.

The spectral entanglement generated by the Hamiltonian in Eq. 3 can be viewed as a consequence of energy and momentum conservation. To quantify these correlations, we rewrite the Hamiltonian in terms of a minimal set of broadband modes via the Schmidt decomposition [41]

{\hat{H}}_{SFWM} = \sum_{m = 1}^{N} c_{m} {\hat{A}}_{m}^{†} (ω_{s}) {\hat{B}}_{m}^{†} (ω_{i}) + H . c .

where

{\hat{A}}_{m}^{†} (ω_{s}) = \int d ω_{s} ξ_{m} (ω_{s}) {\hat{a}}^{†} (ω_{s})

and

{\hat{B}}_{m}^{†} (ω_{i}) = \int d ω_{i} ψ_{m} (ω_{i}) {\hat{a}}^{†} (ω_{i})

. The set of functions {ξ_m}, {ψ_m} are called Schmidt modes, which define an orthonormal basis for the signal and idler Hilbert spaces respectively. This decomposition shows the evolution due to SFWM is equivalent to an ensemble of two-mode squeezing operators e^iĤ_SFWM =Ŝ_A₁,B₁ ⊗ Ŝ_A₂,B₂ ⊗... where Ŝ_{A_m,B_m} is a two-mode squeezing operator on modes A_m and B_m[21].

In general, the Schmidt decomposition in Eq. 4 includes significant contributions from multiple modes so that N > 1. As previously discussed, a detector that cannot resolve these different frequency modes leads to heralding of mixed quantum states. To restore high purity, one can employ spectral filters to remove higher modes but at the cost of reduced count rate. In contrast, the approach we adopt is to design the source to emit only in a single pair of Schmidt modes [12, 16, 17, 42]. This allows heralding of high purity states without filtering. We use the singular value decomposition to numerically perform the Schmidt decomposition in Eq. 4. This allows one to predict the heralded photon purity given source parameters α(ω) and ϕ(ω_s, ω_i) [42].

To investigate the frequency-mode structure of our source, we measure the marginal photon number distribution. An ideal single-mode source would exhibit a thermal distribution, while a highly multi-mode emitter gives Poissonian statistics [43]. In our source, the transition from single-mode to increasingly multi-mode behavior can be readily adjusted via the pump bandwidth Δλ_p[15]. To demonstrate this, we measure the autocorrelation $g_{ss}^{(2)} (0)$ as Δλ_p is varied, as shown in Fig. 3. For Δλ_p = 3.1 nm we measure our optimal $g_{ss}^{(2)} (0) = 1.86 \pm 0.02$ which is close to the ideal thermal result g⁽²⁾(0) = 2. Only APD dark counts are subtracted from the data used to calculate $g_{ss}^{(2)} (0)$ in Fig. 3. One can relate the number of excited Schmidt modes to these statistics using $g_{ss}^{(2)} (0) = 1 + 1 / \sum_{m} {| c_{m} |}^{4} = 1 + P$ where P is the heralded purity. Thus, we have demonstrated P = 0.86 without narrow spectral filtering of the signal and idler modes. To our knowledge, no previous on-chip source has simultaneously demonstrated purities and efficiencies as high as P = 0.86 and η_p = 80%.

Fig. 3 Unheralded $g_{ss}^{(2)} (0)$ of the signal field shows control over the amount of spectral entanglement between the signal and idler fields as Δλ_p is adjusted (brown). Theoretical curve (dotted line) and data (points) are shown. Filtering out the peripheral lobes in the joint spectral intensity with a 4.5 nm filter on the signal field is calculated to give $g_{ss}^{(2)} (0) = 1.98$ at Δλ_p = 3 nm (green dashed line). Insets: joint spectral intensity (JSI) measurements demonstrate spectral entanglement control. The FWHM of the pump envelope |α|⁴ (white) and phase-matching function |ϕ|² (purple) accurately predict JSI orientation.

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The near single-mode emission of our source is further supported by joint spectral intensity measurements. A spectrally uncorrelated state has a factorable joint spectral amplitude, and thus a factorable joint spectral intensity. In the middle inset of Fig. 3, we find that the major and minor axes of the central ellipse are parallel to the λ_i,s axes, which shows a factorable intensity I(λ_i, λ_s) = I_i(λ_i)I_s(λ_s). As Δλ_p is adjusted away from this optimal value, the joint spectral intensities in the left and right insets of Fig. 3 indicate entanglement with an increasingly tilted central lobe. These spectral correlations are in agreement with the measured decrease in $g_{ss}^{(2)} (0)$ .

At the optimal Δλ_p, the slight deviation from ideal thermal statistics, and corresponding reduction in heralded state purity, is principally due to peripheral lobes in the phasematching function. These arise from the hard-edge boundaries of the waveguide and are faintly observed in joint spectral intensity plots. A 4.5 nm filter on λ_s would suppress the small lobes, which would yield $g_{ss}^{(2)} (0) = 1.98$ , and corresponding P = 0.98, while still passing 90% of photons. Such a filter leaves η_P unchanged, as it would only be applied to the heralding signal photon.

Our source offers large spectral tunability of the signal and idler fields. Fig. 4 shows that SFWM is phase-matched over a wide range of pump wavelengths. The inset figures illustrate that over this entire range Δλ_p can be adjusted to achieve factorable output. For larger λ_p the group velocities of the pump and idler photons become comparable, which results in a large spectral bandwidth for the idler. This relatively simple route to broadband emission could be useful, for example in quantum optical coherence tomography [44]. In contrast, many applications, such as quantum memories, instead require narrowband emission. A theory for cavity-enhanced SFWM has been developed that allows emission down to MHz bandwidths [45]. Cavities can be implemented using the refined Bragg grating technology available in silica [46, 47].

Fig. 4 Theoretical phasematching curves show the signal (blue) and idler (red) wavelengths that satisfy the condition Δk = 0 for a range of pump wavelengths. Insets show predicted SFWM joint spectral intensities. A factorable output suitable for heralded production of pure photons can be produced over a wide spectral range, from visible to telecom wavelengths, by adjusting λ_p and Δλ_p (left to right: Δλ_p = 3.1, 7.5, 20 nm). These calculations assume L = 4 cm and Δn = 10⁻⁴.

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5. Birefringence homogeneity

Our analysis so far assumes the waveguide, and thus the wavevectors k_p,s,i, are constant throughout the source. Imperfections in this regard can diminish the purity of heralded photons. Due to our operation of a solid-clad guide far from its zero dispersion wavelength along with the excellent material uniformity of commercial silica [15, 48], the dominant source of inhomogeneity is the birefringence. The spectral output is extremely sensitive to variation in the birefringence since the phase-matched wavelengths depend critically on this parameter [12].

We consider two models of birefringence inhomogeneity and their effect on heralded state purity in Fig. 5. The effects of gradual changes during fabrication, for example variation in the writing laser power or local environment, are modeled as a birefringence that varies linearly along the length of the guide. Rapid fluctuations, on the other hand, are described as a random variation in the birefringence of a specified mean and standard deviation. For both models, the resulting phase-matching function is found by numerically integrating $ϕ (ω_{s}, ω_{i}) = \int_{0}^{L} e^{i z Δ k (z)} d z$ , where Δk(z) has an explicit spatial dependence. The corresponding joint spectral amplitude in Eq. 3 is then used to determine both the heralded purity via the Schmidt decomposition and the joint spectral intensities in the insets of Fig. 5. These simple models suggest our measured purity (gray band, Fig. 5) corresponds to a birefringence inhomogeneity of δ_max(Δn) ≤ 3·10⁻⁶.

Fig. 5 The heralded state purity resulting from two models of birefringence variation are shown. Gradual variation (solid line) is approximated by a linear dependence Δn(z) = Δn₀ + δ (Δn) × z/L. Rapid variation (dashed) is modelled by randomly fluctuating birefringence of mean 〈Δn〉 = Δn₀ and standard deviation δ (Δn). Random inhomogeneity increases the heralded purity for small δ (Δn) due to suppression of the peripheral lobes in the joint spectral amplitude. All results assume L = 4 cm and Δn₀ = 10⁻⁴. Insets show representative joint spectral intensities. The gray shaded region indicates the heralded purity of our source, P = 0.86 ± 0.02.

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Hong-Ou-Mandel interference of two single photons from identical sources produces a visibility equal to the photon purities. Undesirable birefringence variations that reduce heralded purity, as shown in Fig. 5, will therefore reduce interference visibility. In the ideal case of δ (Δn) = 0, using a 4.5 nm filter on the heralding signal photon increases the heralded purity from 0.86 (left side of Fig. 5) to 0.98 while still transmitting 90% of photons. For an inhomogeneity δ (Δn) = 3 · 10⁻⁶, the heralded purity, and thus interference visibility, remains high at 0.95 while the filter transmission is now 84%. Accounting for source inhomogeneity, current fabrication methods thus appear sufficient to obtain high visibility interference from heralded sources.

6. Conclusion

We have demonstrated an on-chip source of heralded single photons that achieves extremely low loss (η_P = 80%) and high output state purity (P = 0.86) without any narrow spectral filtering. To our knowledge, no previous on-chip source has simultaneously demonstrated such low loss heralding of high purity states. Achieving this performance relied on spectrally factorable photon emission which was enabled by the mode control allowed by source integration. An estimate of birefringence inhomogeneity suggests current fabrication methods are sufficient for high visibility interference between multiple sources on the same chip.

Our source meets several loss thresholds for quantum-enhanced applications. Interferometric phase estimation, using single-photon sources with η_P = 80%, can achieve a precision better than any classical probe field with the same number of photons [7]. For linear optics quantum computing, the high η_P and low $g_{H}^{(2)} (0)$ demonstrated here enables entangling gates to violate Bell inequalities without postselection [8]. Exploiting this performance in future work is facilitated by the silica-chip architecture shared by our source and many recent integrated quantum optics experiments [2, 13, 31–35].

In the longer term, multiplexing of sources either spatially with a switching network [49, 50] or temporally with quantum memories [51] may provide a route to construct many-photon quantum states [8, 14]. Even with multiplexing, η_P and P still bound the composite source performance. Therefore, optimizing individual source performance remains critical.

Our choice of SFWM in silica was motivated by the desire to minimize source loss. One direction for future work is to build similar SFWM sources at telecom wavelengths, where silica loss is even lower. As we have shown, the spectral flexibility of SFWM allows factorable states to be generated at these wavelengths with proper adjustment of Δλ_p. Quantum optics experiments in this spectral region, supplied by silica SFWM sources, could investigate a variety of fundamental scientific questions that can feasibly be tested with larger numbers of single photons.

After preparing our manuscript, we learned about concurrent advances in heralded single photon sources by SPDC in a pp-KTP waveguide [52].

We thank Brian Smith, Christoph Söller, and Josh Nunn for valuable insights. This work was supported by the UK EPSRC ( EP/H049037/1, EP/E055818/1 and EP/H03031X/1), the EC project Q-ESSENCE ( 248095), the Royal Society, and the AFOSR EOARD. XMJ and NKL are supported by EU Marie-Curie Fellowships ( PIIF-GA-2011-300820 and PIEF-GA-2010-275103). JBS acknowledges support from the United States Air Force Institute of Technology. The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government.

References and links

1. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001) [CrossRef] [PubMed] .

2. J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013) [CrossRef] .

3. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306, 1330–1336 (2004) [CrossRef] [PubMed] .

4. H. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998) [CrossRef] .

5. M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101 (2011) [CrossRef] [PubMed] .

6. M. Varnava, D. Browne, and T. Rudolph, “How good must single photon sources and detectors be for efficient linear optical quantum computation?” Phys. Rev. Lett. 100, 060502 (2008) [CrossRef] [PubMed] .

7. A. Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, “Quantum metrology with imperfect states and detectors,” Phys. Rev. A 83, 063836 (2011) [CrossRef] .

8. T. Jennewein, M. Barbieri, and A. G. White, “Single-photon device requirements for operating linear optics quantum computing outside the post-selection basis,” J. Mod. Optic. 58, 276–287 (2011) [CrossRef] .

9. M. Lucamarini, G. Vallone, I. Gianani, P. Mataloni, and G. Di Giuseppe, “Device-independent entanglement-based Bennett 1992 protocol,” Phys. Rev. A 86, 032325 (2012) [CrossRef] .

10. D. Bouwmeester, J.-W. Pan, K. Mattle, and M. Eibl, “Experimental quantum teleportation,” Nature 67, 749–752 (1997).

11. M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. J. Wadsworth, and J. G. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17, 4670–4676 (2009) [CrossRef] [PubMed] .

12. C. Söller, O. Cohen, B. J. Smith, I. A. Walmsley, and C. Silberhorn, “High-performance single-photon generation with commercial-grade optical fiber,” Phys. Rev. A 83, 031806 (2011) [CrossRef] .

13. B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013) [CrossRef] [PubMed] .

14. A. Christ and C. Silberhorn, “Limits on the deterministic creation of pure single-photon states using parametric down-conversion,” Phys. Rev. A 85, 023829 (2012) [CrossRef] .

15. B. J. Smith, P. Mahou, O. Cohen, J. S. Lundeen, and I. A. Walmsley, “Photon pair generation in birefringent optical fibers,” Opt. Express 17, 23589–23602 (2009) [CrossRef] .

16. W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A 64, 063815 (2001) [CrossRef] .

17. A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice, and M. G. Raymer, “Generation of pure-state single-photon wavepackets,” Laser Phys. 15, 146–161 (2005).

18. P. J. Mosley, A. Christ, A. Eckstein, and C. Silberhorn, “Direct measurement of the spatial-spectral structure of waveguided parametric down-conversion,” Phys. Rev. Lett. 103, 233901 (2009) [CrossRef] .

19. T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO₄waveguide,” Opt. Express 17, 12019–12030 (2009) [CrossRef] [PubMed] .

20. M. Karpiński, C. Radzewicz, and K. Banaszek, “Dispersion-based control of modal characteristics for parametric down-conversion in a multimode waveguide,” Opt. Lett. 37, 878–880 (2012) [CrossRef] .

21. A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011) [CrossRef] [PubMed] .

22. O. Cohen, J. S. Lundeen, B. J. Smith, G. Puentes, P. J. Mosley, and I. A. Walmsley, “Tailored photon-pair generation in optical fibers,” Phys. Rev. Lett. 102, 123603 (2009) [CrossRef] [PubMed] .

23. F. Zhang and J. W. Y. Lit, “Temperature and strain sensitivity measurements of high-birefringent polarization-maintaining fibers,” Appl. Optics 32, 2213–2218 (1993) [CrossRef] .

24. W. Zou, Z. He, and K. Hotate, “Complete discrimination of strain and temperature using Brillouin frequency shift and birefringence in a polarization-maintaining fiber,” Opt. Express 17, 1248–1255 (2009) [CrossRef] [PubMed] .

25. C. Söller, “Optical fiber sources of pulsed single- and multi-photon states for quantum networks,” Ph.D. thesis, Friedrich-Alexander Universit¨at Erlangen-Nürnberg (2011).

26. C. Xiong, G. D. Marshall, A. Peruzzo, M. Lobino, A. S. Clark, D.-Y. Choi, S. J. Madden, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, T. Zijlstra, V. Zwiller, M. G. Thompson, J. G. Rarity, M. J. Steel, B. Luther-Davies, B. J. Eggleton, and J. L. O’Brien, “Generation of correlated photon pairs in a chalcogenide As₂S₃waveguide,” Appl. Phys. Lett. 98, 051101 (2011) [CrossRef] .

27. M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett. 100, 261104 (2012) [CrossRef] .

28. Q. Lin, F. Yaman, and G. Agrawal, “Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization,” Phys. Rev. A 75, 023803 (2007) [CrossRef] .

29. M. Fiorentino, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photonic. Tech. L. 14, 983–985 (2002) [CrossRef] .

30. K. Inoue and K. Shimizu, “Generation of quantum-correlated photon pairs in optical fiber: Influence of spontaneous Raman scattering,” Jpn. J. Appl. Phys. 43, 8048–8052 (2004) [CrossRef] .

31. G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17, 12546–12554 (2009) [CrossRef] [PubMed] .

32. P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011) [CrossRef] .

33. A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2, 566 (2011) [CrossRef] [PubMed] .

34. J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13, 075003 (2011) [CrossRef] .

35. A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. D. Nicola, F. Sciarrino, and P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013) [CrossRef] .

36. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996) [CrossRef] [PubMed] .

37. G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A-Pure Appl. Op. 11, 013001 (2009) [CrossRef] .

38. P. S. Salter, A. Jesacher, J. B. Spring, B. J. Metcalf, N. Thomas-Peter, R. D. Simmonds, N. K. Langford, I. A. Walmsley, and M. J. Booth, “Adaptive slit beam shaping for direct laser written waveguides,” Opt. Lett. 37, 470–472 (2012) [CrossRef] [PubMed] .

39. R. Loudon, The Quantum Theory of Light(Oxford University, 2000), 3rd ed.

40. D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98% detection efficiency with index-matched small-gap fiber coupling,” Opt. Express 19, 870–875 (2011) [CrossRef] [PubMed] .

41. C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: Effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000) [CrossRef] [PubMed] .

42. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008) [CrossRef] [PubMed] .

43. W. Mauerer, M. Avenhaus, W. Helwig, and C. Silberhorn, “How colors influence numbers: Photon statistics of parametric down-conversion,” Phys. Rev. A 80, 053815 (2009) [CrossRef] .

44. M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultra-broadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. 100, 183601 (2008).

45. K. Garay-Palmett, Y. Jeronimo-Moreno, and A. B. U’Ren, “Theory of cavity-enhanced spontaneous four wave mixing,” Laser Phys. 23, 015201 (2013) [CrossRef] .

46. G. D. Marshall, M. Ams, and M. J. Withford, “Direct laser written waveguide-Bragg gratings in bulk fused silica,” Opt. Lett. 31, 2690–2691 (2006) [CrossRef] [PubMed] .

47. G. Lepert, M. Trupke, E. A. Hinds, H. Rogers, J. C. Gates, and P. G. R. Smith, “Demonstration of UV-written waveguides, Bragg gratings and cavities at 780 nm, and an original experimental measurement of group delay,” Opt. Express 19, 24933–24943 (2011) [CrossRef] .

48. R. H. Stolen, M. A. Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett. 6, 213–215 (1981) [CrossRef] [PubMed] .

49. A. Migdall, D. Branning, and S. Castelletto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A 66, 053805 (2002) [CrossRef] .

50. J. H. Shapiro and F. N. C. Wong, “On-demand single-photon generation using a modular array of parametric downconverters with electro-optic polarization controls,” Opt. Lett. 32, 2698–2700 (2007) [CrossRef] [PubMed] .

51. J. Nunn, N. K. Langford, W. S. Kolthammer, T. F. M. Champion, M. R. Sprague, P. S. Michelberger, X.-M. Jin, D. G. England, and I. A. Walmsley, “Enhancing multiphoton rates with quantum memories,” Phys. Rev. Lett. 110, 133601 (2013) [CrossRef] [PubMed] .

52. G. Harder, V. Ansari, B. Brecht, T. Dirmeier, C. Marquardt, and C. Silberhorn, “An optimized photon pair source for quantum circuits,” arXiv:1304.6635 (2013) [CrossRef] .

On-chip low loss heralded source of pure single photons

Abstract

1. Introduction

2. Experimental overview

3. Nonclassical emission and heralding of single photons

4. Controlling the heralded state purity

5. Birefringence homogeneity

6. Conclusion

References and links

Cited By

Figures (5)

Equations (4)

Optics Express