## Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths |

Optics Express, Vol. 19, Issue 24, pp. 24434-24447 (2011)

http://dx.doi.org/10.1364/OE.19.024434

Acrobat PDF (1572 KB)

### Abstract

We characterize a periodically poled KTP crystal that produces an entangled, two-mode, squeezed state with orthogonal polarizations, nearly identical, factorizable frequency modes, and few photons in unwanted frequency modes. We focus the pump beam to create a nearly circular joint spectral probability distribution between the two modes. After disentangling the two modes, we observe Hong-Ou-Mandel interference with a raw (background corrected) visibility of 86% (95%) when an 8.6 nm bandwidth spectral filter is applied. We measure second order photon correlations of the entangled and disentangled squeezed states with both superconducting nanowire single-photon detectors and photon-number-resolving transition-edge sensors. Both methods agree and verify that the detected modes contain the desired photon number distributions.

© 2011 OSA

## 1. Introduction

*x-*and

*p-*quadratures of the electromagnetic field, and using the variances of these quadratures, one can estimate the purity of a quantum state. The purity is given by

_{tr(ρ2)=1/(2var(x)var(p))}, where var(

*x*) and var(

*p*) are the respective variances, the vacuum quadrature variance is ½, and

*ρ*is the density matrix [2]. The observed purity can be degraded by losses (such as those at free-space optical components and inefficiencies of the photodetectors), electronic noise, and mode-overlap mismatch of a multi-mode squeezed vacuum with the measurement mode,

*i.e.*, the local-oscillator mode. To date, high levels of pure squeezed vacuum have been achieved with cavity squeezing using a CW laser source [3

3. Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, “Observation of -9 dB quadrature squeezing with improvement of phase stability in homodyne measurement,” Opt. Express **15**(7), 4321–4327 (2007). [CrossRef] [PubMed]

4. H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. **100**(3), 033602 (2008). [CrossRef] [PubMed]

*via*photon subtraction [5

5. S. Glancy and H. M. de Vasconcelos, “Methods for producing optical coherent state superpositions,” J. Opt. Soc. Am. B **25**(5), 712–733 (2008). [CrossRef]

7. T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A **82**(3), 031802 (2010). [CrossRef]

*all*the subtracted photons to match the mode of the local oscillator and the mode of the single-mode optical fiber used to spatially filter the subtracted photons.

8. W. P. Grice, A. U’Ren, and I. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A **64**(6), 063815 (2001). [CrossRef]

9. R. S. Bennink and R. W. Boyd, “Improved measurement of multimode squeezed light via an eigenmode approach,” Phys. Rev. A **66**(5), 053815 (2002). [CrossRef]

8. W. P. Grice, A. U’Ren, and I. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A **64**(6), 063815 (2001). [CrossRef]

15. P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright Source of Spectrally Uncorrelated Polarization-Entangled Photons with Nearly Single-Mode Emission,” Phys. Rev. Lett. **105**(25), 253601 (2010). [CrossRef] [PubMed]

*g*

^{(}^{2)}, is another important metric for characterizing the mode structure of squeezed light: mismatch between the signal and idler modes or photons in unwanted modes will cause the measured

*g*

^{(2)}values to depart from theoretical predictions.

## 2. Background

*V*and horizontal

*H*polarizations, which we call the signal and idler beams. The signal and idler may be made of many entangled modes that overlap both in real space and frequency. Ideally the initial multi-mode state is pure, but photon loss will cause decoherence. By collecting the signal and idler with single mode optical fibers, we ensure that all light we detect exists in the same spatial mode. This spatial filtering may cause photon loss, but our measurements are insensitive to loss, so for simplicity we assume that the signal and idler are created in a single spatial mode. In the low squeezing limit, the initial, pure state of the signal and idler is then given by [16

16. A. I. Lvovsky, W. Wasilewski, and K. Banaszek, “Decomposing a pulsed optical parametric amplifier into independent squeezers,” J. Mod. Opt. **54**(5), 721–733 (2007). [CrossRef]

*ξ*is the squeezing parameter, and the state is not normalized. Ψ(

*ω*,

_{s}*ω*) is the signal-idler joint wavefunction, which describes the amplitude distribution for creating a photon pair with signal frequency

_{i}*ω*and idler frequency

_{s}*ω*. This joint wavefunction is determined by both energy conservation and phase-matching conditions, and can be tailored by carefully designing the nonlinear crystal to account for the pump laser’s spectral and spatial mode profiles. Note that higher order terms than those shown in the expansion above are relevant in our experiment, but they are not necessary for this definition of Ψ(

_{i}*ω*,

_{s}*ω*).

_{i}*ω*) with a set of orthogonal modes using the Schmidt decomposition [8

_{s},ω_{i}8. W. P. Grice, A. U’Ren, and I. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A **64**(6), 063815 (2001). [CrossRef]

_{∑nλn=1}. One measure of the quality of the squeezing is the effective mode number,

*K*≥ 1. If only one nonzero coefficient is present (say

*λ*

_{1}= 1), then the two-photon wavefunction is

*factorizable*, Ψ(

*ω*,

_{s}*ω*) =

_{i}*ψ*

_{1}(

*ω*)

_{s}*ϕ*

_{1}(

*ω*), and

_{i}*K*= 1. The effective mode number

*K*is a measure for the number of modes and is therefore not directly linked to the squeezing purity of any single mode (or pair of entangled modes) that can be obtained from homodyne measurements. Unfortunately, measurements of the joint spectral probability distribution, |Ψ(

*ω*

_{s},

*ω*)|

_{i}^{2}, such as those described [11

11. 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**(1), 013603 (2011). [CrossRef] [PubMed]

13. 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**(13), 133601 (2008). [CrossRef] [PubMed]

15. P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright Source of Spectrally Uncorrelated Polarization-Entangled Photons with Nearly Single-Mode Emission,” Phys. Rev. Lett. **105**(25), 253601 (2010). [CrossRef] [PubMed]

*ω*

_{s},

*ω*). As a result,

_{i}*K*can only be computed from joint spectral probability measurements alone by making assumptions about this phase. Here, we perform the Schmidt decomposition of |Ψ(

*ω*

_{s},

*ω*)| and report its effective mode number

_{i}*K*

_{ABS}. If we were to assume that the phase of Ψ(

*ω*,

_{s}*ω*) were constant over all frequencies (or equivalently that |Ψ(

_{i}*ω*

_{s},

*ω*)| were Fourier transform limited in frequency and time), then

_{i}*K*

_{ABS}and

*K*would be identical. Without measuring the phase, we are unable to verify this assumption. While it is the case that all factorizable states must have

*K*=

*K*

_{ABS}= 1, we note that measuring

*K*

_{ABS}= 1 does not necessarily guarantee that

*K*= 1.

*ϕ*

_{1}(

*ω*) =

*ψ*

_{1}(

*ω*), and hence Ψ(

*ω*,

_{s}*ω*) =

_{i}*ψ*

_{1}(

*ω*)

_{s}*ψ*

_{1}(

*ω*). Meeting this condition will allow both signal and idler to be mode-matched to a single local oscillator field.

_{i}## 3. Measurement of the joint spectral probability distribution

### 3.1 Measurement techniques

*H*) and one vertically polarized idler photon (

*V*). To obtain an approximately circular joint spectral probability distribution with degenerate signal and idler photons, we calculated an optimum poling period of 46.55 μm and a crystal length of 2 mm. For a discussion of crystal engineering see [17

17. F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett. **84**(10), 1644 (2004). [CrossRef]

*ϕ*

_{1}(

*ω*) ≈

*ψ*

_{1}(

*ω*). The crystal length was chosen to achieve transform limited signal and idler pairs based on the femtosecond pump’s spectral bandwidth of 5.35 nm (FWHM), and to also match the spectral and temporal bandwidth of the local oscillator field that will be used in future studies.

*V*photons are delayed by approximately 180 ns before being recombined with the

*H*photons at a 50/50 fiber beam splitter. This time-multiplexing allows the detection of both photons with only one single-photon detector, and the 180 ns delay circumvents the ~70 ns single-channel deadtime of the time-stamping electronics. Fewer than 5% of pump pulses generate more than one signal-idler pair.

18. M. G. Tanner, C. M. Natarajan, V. K. Pottapenjara, J. A. O'Connor, R. J. Warburton, R. H. Hadfield, B. Baek, S. Nam, S. N. Dorenbos, E. B. Urena, T. Zijlstra, T. M. Klapwijk, and V. Zwiller, “Enhanced telecom wavelength single-photon detection with NbTiN superconducting nanowires on oxidized silicon,” Appl. Phys. Lett. **96**(22), 221109 (2010). [CrossRef]

19. S. N. Dorenbos, E. M. Reiger, N. Akopian, U. Perinetti, V. Zwiller, T. Zijlstra, and T. M. Klapwijk, “Superconducting single photon detectors with minimized polarization dependence,” Appl. Phys. Lett. **93**(16), 161102 (2008). [CrossRef]

20. M. J. Stevens, R. H. Hadfield, R. E. Schwall, S. W. Nam, R. P. Mirin, and J. A. Gupta, “Fast lifetime measurements of infrared emitters using a low-jitter superconducting single-photon detector,” Appl. Phys. Lett. **89**(3), 031109 (2006). [CrossRef]

^{−1}and 23.6 ± 0.2 ps·nm

^{−1}for the signal and idler path, respectively. Combined with our 1σ temporal resolution of ~28 ps (~65 ps FWHM), this results in 1σ wavelength measurement uncertainties of ~1.2 nm for both the signal and idler paths. In principle, increasing the length of the fiber should improve the spectral resolution; however, our ability to stabilize the fiber temperature, as well as the maximum dispersion set by the repetition rate of the laser will set a practical upper limit on fiber length. A third-order polynomial fitted to the data in Fig. 1(b) determines 1319 ± 0.3 nm as the zero-dispersion-wavelength of this fiber. Determining the spectrum of the signal or idler alone involves acquiring a time-domain histogram proportional to the distribution of arrival times of signal or idler photons with respect to the reference clock signal. An example idler timing-spectrum is shown in Fig. 1(c): in addition to the main parametric down-conversion peak centered close to 1570 nm, there is a weak, broad spectral output, with some detectable light at wavelengths shorter than the zero-dispersion wavelength of 1319 nm. Photons at 1319 nm are the first to arrive at the detector; any photon with a shorter or longer wavelength arrives later, and the spectrum is folded over about this point. The resulting sharp edge in the time-resolved data, identified by the arrow in Fig. 1(c), gives a reference for the absolute wavelength calibration, because it pinpoints the time at which 1319 nm photons arrive at the detector. To measure the joint spectral probability distribution, time-tagged data are post-processed to generate two-dimensional coincidence histograms as a function of both signal and idler wavelengths. Our technique is similar to an earlier approach [14

14. M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. Lett. **34**(18), 2873–2875 (2009). [CrossRef] [PubMed]

14. M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. Lett. **34**(18), 2873–2875 (2009). [CrossRef] [PubMed]

*N*

^{2}reduction in measurement time for an

*N*×

*N*array of signal and idler wavelengths.

### 3.2 Joint spectral probability dependence on pump geometry

*b*

_{c}, (in air) of the focused beams are 0.25 mm, 5.0 mm and 64 mm. These correspond to pump waists

*w*

_{0}of 8 μm, 35 μm and 126 μm, respectively. The insets in Fig. 2(a)-(c) illustrate how the pump beam size changes as it propagates through the crystal for each waist size. All joint spectra were taken with approximately equal measurement times (~4 hours). For the smallest pump waist (Fig. 2(a)), the joint spectrum is elliptical and tilted and therefore is clearly not factorizable. Figures 2(b) and 2(c) show approximately factorizable spectral distributions. However, at the largest pump waist, the photon collection efficiency into the single-mode fiber drops significantly and the data clearly become noisier. This is in qualitative agreement with theoretical results reported by R. Bennink

*et al.*[21

21. R. S. Bennink, “Optimal collinear Gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A **81**(5), 053805 (2010). [CrossRef]

22. A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express **19**(1), 55–65 (2011). [CrossRef] [PubMed]

*H*-polarized signal (blue) and

*V*-polarized idler (red) photons. All single signal and idler spectra were acquired by measuring the arrival times of the signal and idler photons alone, separate from the joint spectral distribution measurement. Because this measurement does not require coincidence events between signal and idler photons, these data have much smaller uncertainties. The signal and idler spectra are approximately mirror images of one another, reflected about a line of symmetry defined by the pump degeneracy point, which is 1570 nm. This mirroring, which is somewhat diminished due to the reduced SNSPD detection efficiency at longer wavelengths (lower frequencies) [18

18. M. G. Tanner, C. M. Natarajan, V. K. Pottapenjara, J. A. O'Connor, R. J. Warburton, R. H. Hadfield, B. Baek, S. Nam, S. N. Dorenbos, E. B. Urena, T. Zijlstra, T. M. Klapwijk, and V. Zwiller, “Enhanced telecom wavelength single-photon detection with NbTiN superconducting nanowires on oxidized silicon,” Appl. Phys. Lett. **96**(22), 221109 (2010). [CrossRef]

*H*and

*V*photons can be seen from the separation of the individual peaks. For the smallest pump waist we observe a separation of ~6 nm. This decreases to ~4 nm for the intermediate beam waist, and approximately degenerate spectra are achieved for the largest pump waist, demonstrating |

*ϕ*

_{1}(

*ω*)|

^{2}≈|

*ψ*

_{1}(

*ω*)|

^{2}. A possible reason for the shift from the degeneracy point to non-degenerate pairs is the contribution of higher-order spatial modes that overlap with the spatial mode of our single-mode fiber. A more uniform pump waist inside the crystal thus yields a higher degree of degeneracy, but at the expense of reduced pump fluence and reduced fiber coupling efficiency of the photon pairs.

### 3.3 The effect of spectral filtering on the joint spectral probability density and Schmidt decomposition

*ω*

_{s},

*ω*)|, calculated from the measured joint-probability distribution, and (b) the individual signal and idler spectra (measured by determining the single photons’ arrival times), all for a pump waist of ~50 μm (

_{i}*b*= 10 mm) and without spectral filtering. The maxima of the signal and idler spectra are separated by approximately 2 nm (determined from the peak separation of the two Gaussian fits): the spectral bandwidth and center wavelengths are 20.1 nm (20.5 nm) and 1569 nm (1571 nm) for the

_{c}*H*(

*V*) photons. The spectral decomposition of the absolute value of the joint spectral amplitude distribution yields

*K*

_{ABS}= 1.06 ± 0.02. The uncertainties for all the reported effective mode numbers were found by parametric bootstrap resampling [23].

*ω*

_{s},

*ω*)| yields a slightly larger

_{i}*K*

_{ABS}= 1.08 ± 0.02 than in the unfiltered case, but the signal and idler are closer to being fully degenerate. One can observe a slightly elliptical output joint spectrum in both cases, which was caused by a change in the bandwidth of the pump laser in the cavity-dumped configuration [14

14. M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. Lett. **34**(18), 2873–2875 (2009). [CrossRef] [PubMed]

## 4. Hong-Ou-Mandel interference

*V*mode is rotated by 90° with a half-waveplate (

*λ*/2), and signal and idler are then recombined on a 50/50 beam splitter. A computer-controlled translation stage varies the arrival time (Δ

*t*) at the beam splitter of photons in mode

*H*. Each output mode (

*c*and

*d*) of the 50/50 beam splitter is coupled into a single-mode fiber and the collected photons are delivered to a photon-number-resolving, superconducting transition-edge sensor (TES) [24

24. A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express **16**(5), 3032–3040 (2008). [CrossRef] [PubMed]

*c*and

*d*, respectively. (The reason for the lower detection efficiency of one detector is that this detector was optimized for a wavelength band around 800 nm, yielding a lower efficiency at 1550 nm).

*n*= 0, 1, 2,...) in each mode. A coincidence is an event in which both detectors record

*n*≥ 1 photons for the same pump pulse. These coincidences are recorded as a function of Δ

*t*. The increased timing jitter (~100 ns) of the TES dictates that we perform this experiment with the cavity-dumped pulse train, at a repetition rate of 456 kHz.

*K*would likely cause a decrease of the HOM interference visibility, because not all signal and idler mode pairs would be fully degenerate. We compare the visibility of our HOM interference with the overlap integral of the measured signal and idler photons’ spectra shown in Fig. 3(d) [13

13. 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**(13), 133601 (2008). [CrossRef] [PubMed]

_{|∫|Ψ(ω)||φ(ω)|dω|2}≈98%. (Note that this is only an estimate. A full calculation of the visibility would require knowledge of the joint spectral amplitude, but we only know its absolute value. Also, the full calculation should consider entanglement between the signal and idler photons’ wave functions, which we have neglected here.) This value roughly agrees with the corrected HOM visibility. Multi-pair generation in the pp-KTP crystal is also expected to further reduce the HOM visibility, since the HOM effect predicts full coincidence suppression only when exactly one photon is present at each input of the 50/50 beam splitter [25

25. O. Kuzucu and F. N. C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A **77**(3), 032314 (2008). [CrossRef]

26. T. Zhong, F. N. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO4 waveguide,” Opt. Express **17**(14), 12019–12030 (2009). [CrossRef] [PubMed]

## 5. Second-order correlation measurements

*j*and

*k*at zero time delay is defined to beWhen

*j*=

*k*, we refer to the

*g*

_{ij}^{(2)}as the autocorrelation, and for

*j*≠

*k*it is the cross-correlation.

*g*

^{(2)}is insensitive to linear photon loss (provided that all modes are subjected to the same loss), so it can be a useful diagnostic tool regardless of the efficiency of the photon detection systems, but it is unable to distinguish between a pure squeezed state and the same squeezed state subject to loss (or a similar effect).

*g*

^{(2)}uses a standard photon-correlation scheme with two SNSPDs and time-domain histogramming electronics. A photon detected by one SNSPD starts a timer, which is then stopped after a time delay

*τ*, once the other SNSPD detects a photon. The resulting histogram of start-stop pairs is proportional to

*g*

^{(2)}(

*τ*). Figure 5(a) shows an example time-domain histogram. To determine the zero delay value,

*g*

^{(2)}, we take the area of the peak at zero delay (identified by the large peak in Fig. 5(a)) and divide by the average area of the surrounding peaks. To find the autocorrelation of a single mode,

*g*

_{jj}^{(2)}, we place a 50/50 beam splitter in mode

*j*, and place one SNSPD at each output port of the beam splitter. The configuration for measuring

*g*

_{HH}^{(2)}in this way is shown in Fig. 5(e). To find the cross-correlation between two different modes,

*g*

_{jk}^{(2)}for

*j*≠

*k*, we place one SNSPD in mode

*j*and the other in mode

*k*, as shown in Fig. 5(f) for

*g*

_{HV}^{(2)}. When measuring

*g*

_{jk}^{(}^{2)}by time-domain histogram we use the direct 76 MHz output of the Ti:Sapphire oscillator.

*p*represents the probability of detecting

_{n}*n*photons from any given pump pulse. (We do not use this method for cross-correlation.) Fig. 5(b) shows an example photon-number probability distribution. For clarity, we have not plotted the vacuum contribution to this distribution, but it can be easily computed as

_{p0=1−∑n=1∞pn}. Due to the slow response of the TES, when we measure

*g*

_{jj}^{(2)}via photon-number probabilities, we operate with the cavity dumped output at 360 kHz.

*H*and

*V*modes of an ideal two-mode squeezer, we expect [28

28. J. Xiong, G. Zeng, and N. Zhou, “An improved quantum key distribution protocol based on second-order coherence,” Opt. Commun. **260**(1), 351–354 (2006). [CrossRef]

*n*〉 is the mean number of photons generated per pump pulse. If multiple modes are present,

*g*

_{HH}^{(2)}is expected to be smaller, approaching 1 as the number of modes approaches infinity. A diagram of this measurement is in Fig. 5(f). The result of this measurement is shown for several 〈

*n*〉 values in Fig. 5(c) with black circles. The black curve is a plot of Eq. (6) to this data. Note that we estimated the proportionality constant between pulse energy and generated mean photon number. We used this proportionality constant to plot Eq. (6) and (8) (red and black lines in Fig. 5)

*n*〉. Values for

*g*

_{HH}^{(2)}obtained using both time-domain histograms measured by SNSPD (as shown in Fig. 5(e)) and photon-number probabilities measured by TES appear in Fig. 5(c) and (d). The results from both methods are in close agreement. We would expect the presence of multiple squeezed modes entering the detectors to decrease the value of

*g*

_{HH}^{(2)}from 2 to 1 + 1/

*K*, and this property was used to estimate

*K*in [11

11. 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**(1), 013603 (2011). [CrossRef] [PubMed]

*g*

_{HH}^{(2)}to be somewhat higher than 2 at the lowest pump powers; this is likely due to experimental imperfections that cause some

*V*photons to scatter into the

*H*output port of the polarizing beam splitter. This problem is worse at small 〈

*n*〉 simply because the bunching between

*H*and

*V*is much more pronounced as 〈

*n*〉 decreases, as is evident in the

*g*

_{HV}^{(2)}data.

*H*and

*V*experience HOM interference as in Fig. 4(a), we expect a single-mode squeezed vacuum in each output port of the 50/50 beam splitter [29

29. J. Xiong, N. Zhou, and G. Zeng, “Second-order coherence of light fields with a beam splitter,” J. Phys. B **38**(23), 4301–4308 (2005). [CrossRef]

*g*

_{cc}^{(2)}obtained using the TES measurement of photon probabilities are shown in Fig. 5(c) with red circles, and the red line is the plot of Eq. (8). Again we see good agreement with expectations.

## 6. Summary

*g*

^{(2)}values fit the theoretical predictions of single-mode outputs (thermal and squeezed vacuum) very well. All of these results give evidence that we have successfully created entangled squeezed signal and idler beams with nearly identical, factorizable, spatio-temporal modes. They also show that very little squeezed light is created in unwanted modes that are also collected by our photon detectors. We have employed advanced photon-counting techniques based on superconducting detectors (SNSPDs and TESs) to characterize the single-mode character of two-mode and single-mode squeezed states. These techniques are useful tools for investigating the spatial-mode properties of the squeezing. In the near future, we plan to map the local oscillator mode-matching characteristics and the squeezing purity of this source using homodyne detection.

## Acknowledgements

## References and links

1. | C. Gerry and P. Knight, |

2. | U. Leonhardt, |

3. | Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, “Observation of -9 dB quadrature squeezing with improvement of phase stability in homodyne measurement,” Opt. Express |

4. | H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. |

5. | S. Glancy and H. M. de Vasconcelos, “Methods for producing optical coherent state superpositions,” J. Opt. Soc. Am. B |

6. | A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrödinger Kittens for Quantum Information Processing,” Science |

7. | T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A |

8. | W. P. Grice, A. U’Ren, and I. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A |

9. | R. S. Bennink and R. W. Boyd, “Improved measurement of multimode squeezed light via an eigenmode approach,” Phys. Rev. A |

10. | O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett. |

11. | 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. |

12. | X. Shi, A. Valencia, M. Hendrych, and J. P. Torres, “Generation of indistinguishable and pure heralded single photons with tunable bandwidth,” Opt. Lett. |

13. | 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. |

14. | M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. Lett. |

15. | P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright Source of Spectrally Uncorrelated Polarization-Entangled Photons with Nearly Single-Mode Emission,” Phys. Rev. Lett. |

16. | A. I. Lvovsky, W. Wasilewski, and K. Banaszek, “Decomposing a pulsed optical parametric amplifier into independent squeezers,” J. Mod. Opt. |

17. | F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett. |

18. | M. G. Tanner, C. M. Natarajan, V. K. Pottapenjara, J. A. O'Connor, R. J. Warburton, R. H. Hadfield, B. Baek, S. Nam, S. N. Dorenbos, E. B. Urena, T. Zijlstra, T. M. Klapwijk, and V. Zwiller, “Enhanced telecom wavelength single-photon detection with NbTiN superconducting nanowires on oxidized silicon,” Appl. Phys. Lett. |

19. | S. N. Dorenbos, E. M. Reiger, N. Akopian, U. Perinetti, V. Zwiller, T. Zijlstra, and T. M. Klapwijk, “Superconducting single photon detectors with minimized polarization dependence,” Appl. Phys. Lett. |

20. | M. J. Stevens, R. H. Hadfield, R. E. Schwall, S. W. Nam, R. P. Mirin, and J. A. Gupta, “Fast lifetime measurements of infrared emitters using a low-jitter superconducting single-photon detector,” Appl. Phys. Lett. |

21. | R. S. Bennink, “Optimal collinear Gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A |

22. | A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express |

23. | B. Efron and R. J. Tibshirani, |

24. | A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express |

25. | O. Kuzucu and F. N. C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A |

26. | T. Zhong, F. N. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO4 waveguide,” Opt. Express |

27. | R. Loudon, |

28. | J. Xiong, G. Zeng, and N. Zhou, “An improved quantum key distribution protocol based on second-order coherence,” Opt. Commun. |

29. | J. Xiong, N. Zhou, and G. Zeng, “Second-order coherence of light fields with a beam splitter,” J. Phys. B |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5290) Quantum optics : Photon statistics

(270.5570) Quantum optics : Quantum detectors

(270.6570) Quantum optics : Squeezed states

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: August 3, 2011

Revised Manuscript: October 25, 2011

Manuscript Accepted: October 27, 2011

Published: November 15, 2011

**Citation**

Thomas Gerrits, Martin J. Stevens, Burm Baek, Brice Calkins, Adriana Lita, Scott Glancy, Emanuel Knill, Sae Woo Nam, Richard P. Mirin, Robert H. Hadfield, Ryan S. Bennink, Warren P. Grice, Sander Dorenbos, Tony Zijlstra, Teun Klapwijk, and Val Zwiller, "Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths," Opt. Express **19**, 24434-24447 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24434

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### References

- C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2004).
- U. Leonhardt, Measuring The Quantum State Of Light (Cambridge University Press, 1997).
- Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, “Observation of -9 dB quadrature squeezing with improvement of phase stability in homodyne measurement,” Opt. Express15(7), 4321–4327 (2007). [CrossRef] [PubMed]
- H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett.100(3), 033602 (2008). [CrossRef] [PubMed]
- S. Glancy and H. M. de Vasconcelos, “Methods for producing optical coherent state superpositions,” J. Opt. Soc. Am. B25(5), 712–733 (2008). [CrossRef]
- A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrödinger Kittens for Quantum Information Processing,” Science312(5770), 83–86 (2006). [CrossRef] [PubMed]
- T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82(3), 031802 (2010). [CrossRef]
- W. P. Grice, A. U’Ren, and I. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64(6), 063815 (2001). [CrossRef]
- R. S. Bennink and R. W. Boyd, “Improved measurement of multimode squeezed light via an eigenmode approach,” Phys. Rev. A66(5), 053815 (2002). [CrossRef]
- O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett.101(15), 153602 (2008). [CrossRef] [PubMed]
- 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(1), 013603 (2011). [CrossRef] [PubMed]
- X. Shi, A. Valencia, M. Hendrych, and J. P. Torres, “Generation of indistinguishable and pure heralded single photons with tunable bandwidth,” Opt. Lett.33(8), 875–877 (2008). [CrossRef] [PubMed]
- 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(13), 133601 (2008). [CrossRef] [PubMed]
- M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. Lett.34(18), 2873–2875 (2009). [CrossRef] [PubMed]
- P. G. Evans, R. S. Bennink, W. P. Grice, T. S. Humble, and J. Schaake, “Bright Source of Spectrally Uncorrelated Polarization-Entangled Photons with Nearly Single-Mode Emission,” Phys. Rev. Lett.105(25), 253601 (2010). [CrossRef] [PubMed]
- A. I. Lvovsky, W. Wasilewski, and K. Banaszek, “Decomposing a pulsed optical parametric amplifier into independent squeezers,” J. Mod. Opt.54(5), 721–733 (2007). [CrossRef]
- F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett.84(10), 1644 (2004). [CrossRef]
- M. G. Tanner, C. M. Natarajan, V. K. Pottapenjara, J. A. O'Connor, R. J. Warburton, R. H. Hadfield, B. Baek, S. Nam, S. N. Dorenbos, E. B. Urena, T. Zijlstra, T. M. Klapwijk, and V. Zwiller, “Enhanced telecom wavelength single-photon detection with NbTiN superconducting nanowires on oxidized silicon,” Appl. Phys. Lett.96(22), 221109 (2010). [CrossRef]
- S. N. Dorenbos, E. M. Reiger, N. Akopian, U. Perinetti, V. Zwiller, T. Zijlstra, and T. M. Klapwijk, “Superconducting single photon detectors with minimized polarization dependence,” Appl. Phys. Lett.93(16), 161102 (2008). [CrossRef]
- M. J. Stevens, R. H. Hadfield, R. E. Schwall, S. W. Nam, R. P. Mirin, and J. A. Gupta, “Fast lifetime measurements of infrared emitters using a low-jitter superconducting single-photon detector,” Appl. Phys. Lett.89(3), 031109 (2006). [CrossRef]
- R. S. Bennink, “Optimal collinear Gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A81(5), 053805 (2010). [CrossRef]
- A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express19(1), 55–65 (2011). [CrossRef] [PubMed]
- B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Capman & Hall, 1993).
- A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express16(5), 3032–3040 (2008). [CrossRef] [PubMed]
- O. Kuzucu and F. N. C. Wong, “Pulsed Sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A77(3), 032314 (2008). [CrossRef]
- T. Zhong, F. N. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO4 waveguide,” Opt. Express17(14), 12019–12030 (2009). [CrossRef] [PubMed]
- R. Loudon, The Quantum Theory of Light (Oxford University Press, 2004).
- J. Xiong, G. Zeng, and N. Zhou, “An improved quantum key distribution protocol based on second-order coherence,” Opt. Commun.260(1), 351–354 (2006). [CrossRef]
- J. Xiong, N. Zhou, and G. Zeng, “Second-order coherence of light fields with a beam splitter,” J. Phys. B38(23), 4301–4308 (2005). [CrossRef]

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