J. Vis. Exp. (87), e51224 5/30/2014jove.come/video/51224

chistera-qscale.eu/jove.html

Quantum state engineering of light withcontinuous-wave optical parametric oscillatorsOlivier Morin1, Jianli Liu1, Kun Huang1,2, Felippe Barbosa3, Claude Fabre1, Julien Laurat1*

AbstractThe ability to engineer the quantum state of traveling optical fields is a central requirement for quantuminformation science and technology, including quantum communication, computing and metrology. In thisvideo article, we describe the reliable generation of non-Gaussian states, including single-photon states andcoherent state superpositions, using a conditional preparation method operated on the non-classical lightemitted by optical parametric oscillators. Type-I and type-II phase-matched OPOs operated below threshold,i.e. single-mode or two-mode squeezed vacuum sources, are considered and common procedures, suchas the required frequency filtering or the high-efficiency quantum state characterization by homodyning, aredetailed. The reported method enables a high fidelity with the targeted state and the generation of the state in awell-controlled spatiotemporal mode, a crucial feature for their use in subsequent protocols.

The video of this article can be found at jove.come/video/51224 or chistera-qscale.eu/jove.html

KeywordsQuantum optics, Quantum state engineering, Optical parametric oscillator, Squeezed vacuum, Single photon,Coherent state superposition, Homodyne detection

1Laboratoire Kastler Brossel, Université Pierre et Marie Curie, Ecole Normale Supérieure, CNRS, 4 place Jussieu, 75252 Paris Cedex 05,France2State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China2Instituto de Física, Universidade de São Paulo P. O. Box 66318, São Paulo, SP 05314- 970, Brazil*Corresponding author: julien.laurat@upmc.fr

1. IntroductionThe ability to engineer the quantum state of traveling opticalfields is a central requirement for quantum information scienceand technology [1, 2], including quantum communication,computing and metrology. Here, we discuss the preparationand characterization of some specific quantum states usingas a primary resource the light emitted by continuous-waveoptical parametric oscillators [3, 4] operated below threshold.Specifically, two systems will be considered, a type-II phase-matched OPO and a type-I OPO , enabling respectively thereliable generation of heralded single-photons and of opticalcoherent state superpositions (CSS), i.e. states of the form|α〉 − |−α〉. These states are important resources for theimplementation of a variety of quantum information protocols,ranging from linear optical quantum computation [5] to opticalhybrid protocols [6, 7]. Significantly, the method presentedhere permits obtaining a low admixture of vacuum and theemission into a well-controlled spatiotemporal mode.

Generally speaking, quantum states can be classified asGaussian states and non-Gaussian states according to theshape of the quasi- probability distribution in phase spacecalled the Wigner function W(x, p) [8]. For non-Gaussianstates, the Wigner function can take negative values, a strong

signature of non-classicality. Single-photon or coherent statesuperpositions are indeed non-Gaussian states. An efficientprocedure for generating such states is known as the condi-tional preparation technique, where an initial Gaussian re-source is combined with a so-called non-Gaussian measure-ment such as photon counting [9, 10, 11, 12, 13]. This generalscheme, probabilistic but heralded, is sketched on Figure 1a.By measuring one mode of a bipartite entangled state, theother mode is projected into a state that will depend on thismeasurement and on the initial entangled resource [12, 13].

What are the required resource and heralding detectorneeded to generate the aforementioned states? Single-photonstates can be generated using twin beams, i.e. photon-numbercorrelated beams. The detection of a single-photon on onemode then heralds the generation of a single- photon on theother mode [9, 10, 14, 15]. A frequency-degenerate type-IIOPO [16, 17, 18, 19] is indeed a well-suited source for thispurpose. Signal and idler photons are photon-number corre-lated and emitted with orthogonal polarizations. Detecting asingle-photon on one polarization mode projects the other oneinto a single-photon state, as shown in Figure 1b.

Concerning coherent state superpositions, they can begenerated by subtracting a single-photon from a squeezed

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Figure 1. Conditional state preparation technique.(a) Conceptual scheme. (b) Conditional preparation ofsingle-photon state from orthogonally-polarized photon pairs(type-II OPO) separated on a polarizing beam splitter. (c)Conditional preparation of a coherent state superposition bysubtracting a single-photon from a squeezed vacuum state(type-I OPO).

vacuum state [20] obtained either by pulsed single-pass para-metric down-conversion [11, 21] or by a type-I OPO [22, 23].The subtraction is performed by tapping a small fraction of thelight on a beam-splitter and detecting a single-photon in thismode (Figure 1c). A squeezed vacuum is a superposition ofeven photon- number states, thus subtracting a single-photonleads to a superposition of odd photon-number states, whichhas a high fidelity with a linear superposition of two coherentstates of equal and small amplitude. For this reason, the nameSchrödinger kitten has sometimes been given to this state.

The general procedure for generating these states is thussimilar, but differs by the primary light source. Filtering ofthe heralding path and detection techniques are the same what-ever the type of OPO used. The present series of protocolsdetail how to generate these two non- Gaussian states fromcontinuous-wave optical parametric oscillators and how tocharacterize them with high efficiency.

2. Protocol2.1 Optical Parametric Oscillator• Build a 4 cm long semimonolithic linear cavity (for

improved mechanical stability and reduced intracavitylosses). The input mirror is directly coated on one faceof the nonlinear crystal.

• Choose an input coupler reflection of 95% for the pumpat 532 nm and high-reflection for the signal and idlerat 1064 nm. Inversely, choose the output coupler tobe highly reflective for the pump and of transmittanceT=10% for the infrared. The free spectral range of theOPO is equal to ∆ω = 4.3 GHz and the bandwidth isaround 60 MHz. Make the cavity triply resonant, i.e.for the pump and for the down-converted fields.

• Use a KTP crystal for the type-II OPO system or a PP-KTP crystal for the type-I OPO. Temperature-stabilizethe crystals at their phase- matching temperatures.

• Use as laser source a continuous-wave frequency dou-bled Nd:YAG laser. Pump the OPO at 532 nm and usethe infrared light, after spatial filtering by a high-finessecavity (mode cleaner), as a local oscillator (LO) for thehomodyne detection.

• Achieve the mode-matching between the pump and thecavity mode.

• Lock the cavity length on the pump resonance by thePound-Drever-Hall technique. For this purpose, applya 12 MHz electro-optic modulation to the pump anddetect the light back-reflected from the cavity with anoptical isolator.

2.2 Conditional Preparation: filtering the HeraldingPath• Separate the OPO output into two modes. One corre-

sponds to the heralding mode, while the other one is theheralded state that will be detected by the homodynedetection.

• Guide the heralding mode towards the single-photondetector. Specifically, for the type-II OPO, separatethe orthogonal signal and idler modes by a polarizedbeam splitter (PBS). For the type-I OPO, tap out a smallfraction (3%) of the squeezed vacuum by a beam splitter(BS).

• Filter the heralding mode to remove the frequency non-degenerate modes due to the OPO cavity. For an OPO,the output indeed contains many pairwise correlated butspectrally separated modes, ω0 +n∆ω and ω0−n∆ω

where n is an integer. To generate a heralded state atthe carrier frequency, it is necessary to filter out all ofthese non-degenerate modes.

Quantum state engineering of light with continuous-wave optical parametric oscillators — 3/6

– Use first an interferential filter with a bandwidthof 0.5 nm.

– Add a homemade linear Fabry-Perot cavity witha free spectral range of 330 GHz and a bandwidthof 300 MHz (length around 0.4 mm and finessearound 1000). The cavity bandwidth is chosento be larger than the one of the OPO and the freespectral range to be larger than the frequency win-dow of the interferential filter.

– Achieve at least an overall 25 dB rejection of thenon-degenerate modes.

• Lock the filtering Fabry-Perot cavity by the dither-and-lock technique.

– For this purpose, inject a backward propagatingauxiliary beam via an optical switch and reject itat the entrance of the filtering cavity by an opticalisolator. Detect the light at the output.

– Lock the cavity during 10 msec and start afterthe measurement period for 90 msec with theauxiliary-beam off.

• Detect the filtered heralding mode by a single-photondetector during the measurement period. A supercon-ducting single-photon detector (SSPD) is used to limitthe amount of dark noise (few Hz), which otherwisewould degrade the fidelity of the conditional state.

2.3 Quantum State Tomography by Homodyne De-tection• Detect the heralded state with a balanced homodyne

detection composed of a 50/50 beam splitter where thefield to characterize and a strong continuous-wave localoscillator (LO, 6 mW) are brought to interfere, and apair of high quantum efficiency InGaAs photodiodes.

• In order to align the detection, inject into the OPO cav-ity a bright auxiliary beam at 1064 nm and mode matchthis mode with the LO mode. Achieve a fringe visibil-ity close to unity. Any mode mismatch quadraticallytranslates into detection losses.

• Check the homodyne detection properties. With a LOpower of 6 mW, the shot noise limit (SNL) is flat upto 50 MHz. It is more than 20 dB above the electronicnoise at low analysis frequency (MHz), 16 dB aboveat the analysis frequency of 50 MHz. This distance isa critical parameter as it translates into losses in thedetection (a 10 dB (20 dB) distance translates into a10% (1%) effective loss) [24].

• For every detection event from the single-photon detec-tor, record the homodyne photocurrent with an oscil-loscope with a sampling rate of 5 Gs/sec during 100nsec. Sweep the LO phase with a PZT-mounted mirrorduring the measurement.

• Filter each recorded segment with a given temporalmode function to obtain at each successful preparationa single quadrature value of the conditional state. Theoptimal mode function for low gain is close to a double-sided exponential function [25] with a decay constantequal to the inverse of the OPO bandwidth. The opti-mal mode can also be found by using a eigenfunctionexpansion of the autocorrelation function [26].

• Accumulate measurements (50000 are required for thetomography) and post-process the data with a maximum-likelihood algorithm [27]. This procedure enables re-construction of the density matrix of the heralded stateand the corresponding Wigner function [8].

2.4 Conditional Preparation of single Photon Statewith a type-II OPO• Pump the type-II OPO far below threshold (1 mW here

for a 80 mW threshold) to have a very low probabilityof multiphoton pairs.

2.5 Conditional Preparation of Coherent State Su-perposition with a type-I OPO• Check the squeezed vacuum generated by the OPO

close to threshold with a spectrum analyzer. The mea-sured noise spectra are shown in Figure 3.

• Operate the OPO at a pump power enabling observationof around 3 dB of squeezing at low sideband frequen-cies (few MHz).

• In the homodyne measurement, the phase informationis important for phase-dependent states such as the CSSstate. Scan the LO phase with a 10 Hz sawtooth wavewith a duty cycle of 90% (corresponding to the 90 msecof measurement period and 10 msec of locking period.)Synchronize the sweep to make sure that during themeasurement period, there is a single one-directionalsweep of the PZT-mounted mirror.

• Use the homodyne signal to measure the variance andthen infer the phase of the measured quadrature.

3. Representative Results

3.1 For the type-II OPO and the generation of high-fidelity single photon state

The tomographic reconstruction of the heralded state is shownin Figure 2, where the diagonal elements of the reconstructeddensity matrix and the corresponding Wigner function aredisplayed. Without any loss corrections, the heralded stateexhibits a single-photon component as high as 78%. By tak-ing into account the overall detection losses (15%), the statereaches a fidelity of 91% with a single-photon state. The two-photon component, which results from multi-photon pairscreating by the down conversion process, is limited to 3%.

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Figure 2. High-fidelity single-photon state. (a) Diagonalelements of the reconstructed density matrix withoutcorrection from detection losses. (b) Corresponding Wignerfunction. x and p denote quadrature components.

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Figure 4. Coherent state superposition (Schrödingerkitten state). (a) Diagonal elements of the reconstructeddensity matrix without correction from detection losses. (b)Corresponding Wigner function. x and p denote quadraturecomponents.

3.2 For the type-I OPO and the generation of CSSstate

The threshold of the type-I OPO is about 50 mW. In order toobserve strong squeezing, we perform measurements close tothreshold, i.e. with a pump power of 40 mW, and at an analysisfrequency of 5 MHz. As shown in Figure 3a, the measuredsqueezing is -10.5 ± 0.5 dB relative to the shot noise (withoutany corrections, 16 ± 1 dB if corrected for detection loss andelectronics noise), and the anti-squeezing is 19 ± 0.5 dB. Thefull noise spectra from 0 to 50 MHz at pump power of 40mW and 5 mW is shown in Figure 3b. At a pump power of 5mW, the values of squeezing and anti-squeezing are nearly thesame, leading to a state with a purity close to unity. This high-purity squeezed vacuum state is used to prepare the CSS state.The tomographic reconstruction of the heralded state is givenin Figure 4, where the diagonal elements of the reconstructeddensity matrix and the corresponding Wigner function aredisplayed.

4. DiscussionThe conditional preparation technique presented here is al-ways an interplay between the initial bipartite resource andthe measurement performed by the heralding detector. Thesetwo components strongly influence the quantum properties ofthe generated state.

First, the purity of the prepared states strongly depends on

the one of the initial resource, thus a good OPO is required.What is a good OPO? It is a device for which the escapeefficiency η is close to unity. The parameter η is given bythe ratio of the transmission of the output coupler T , and thesum of this transmission and the intra-cavity losses (comingfrom scatterings or absorption in the crystal), L+T . For agiven L, the transmission of the output should be increased,at the expense of a threshold increasing quadratically withthis transmission. The escape efficiency directly defines themaximal amount of squeezing that can be obtained closeto threshold. Here, the escape efficiency is about 96% forboth OPO. For the conditional preparation, the OPO is thenoperated far from the threshold to guarantee a high purity.

Another factor comes from the heralding single-photondetection. First of all, current single-photon detectors aremostly on/off detectors, only able to herald the detection ofat least 1 photon. For this reason, it is crucially important tobe in a regime where the probability to have two photons inthe conditioning path is very low compare to the probabilityto have one photon. Secondly, detectors can be noisy. Suchevents do not herald the generation of the targeted state andresult in a mixture of the heralded state and the initial resource.Specifically, they would lead to an admixture of vacuum in thesingle-photon preparation or of squeezed vacuum in the CSSpreparation. In our experiment, we use a superconductingsingle-photon detector to limit this contribution. The darknoise is around a few hertz (whereas single-photon count rateis tens of kHz).

The method presented here enables the reliable generationof non-Gaussian states with a high-fidelity, mainly limited bythe losses in the detection due to the close to unity escapeefficiency of the OPO. Furthermore, the well-controlled spa-tiotemporal mode in which they are generated will facilitatetheir use in subsequent protocols where such states may needto interfere with other optical resources, e.g. in optical gateimplementations [28] or complex state engineering [29].

AcknowledgmentsThis work is supported by the ERA-NET CHIST-ERA (QS-cale) and by the ERC starting grant HybridNet. F. Barbosaacknowledges the support from CNR and FAPESP, and K.Huang the support from the Foundation for the Author of Na-tional Excellent Doctoral Dissertation of China (PY2012004)and the China Scholarship Council. C. Fabre and J. Laurat aremembers of the Institut Universitaire de France.

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