Extended phase-matching conditions for improved entanglement generation

Two-photon states entangled in continuous variables such as wavevector or frequency represent a powerful resource for quantum information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several non-overlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comb-like spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of non-overlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.PACS numbers: 42.50. Dv, 42.50.Ar, 03.65.Ta, 85.60.Gz Introduction.Entanglement of two-photon states (biphotons) in continuous variables such as frequency or wavevector suggests the use of biphotons as a quantum-information resource in higher-dimensional Hilbert spaces [1,2]. The dimensionality of the Hilbert space is determined in this case by the Schmidt number, the effective number of Schmidt modes, which can reach several hundred [2][3][4]. But in order to realize any protocols with multimode states, it is necessary to address single Schmidt modes separately. For wavevector variables, any single Schmidt mode can be filtered out using a single-mode fibre and a spatial light modulator [6]. This filtering, in principle, can be lossless, which is crucial for experiments with twin-beam squeezing [7][8][9][10][11][12]. For frequency variables, it is far more difficult to losslessly select a single Schmidt mode. Attempts are being made in homodyne detection [13]; in direct detection experiments the procedure is more difficult. For instance, methods based on nonlinear frequency conversion are proposed, technically complicated to realize with high efficiency [14]. Here we propose and demonstrate a method of engineering a two-photon state in such a way that it contains non-overlapping Schmidt modes, each of which can be filtered losslessly using a spectral device.Frequency entanglement of biphotons. A two-photon state generated via SPDC can be written in the formwhereâ † s ,â † i are the creation operators of the signal and idler photons, and F (ω s , ω i ) represents the two-photon spectral amplitude (TPSA) [15]. The TPSA fully characterizes the spectral properties of a biphoton state and its physical meaning is the joint spectral probability amplitude of the down-converted photons in signal and idler modes with frequencies ω s and ω i respectively. TPSA is used to determine the degree of frequency entanglemen...

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“…The possibility of a positive tilt, first discussed in Ref. [23], is realized in KDP at higher pumping wavelengths. The tilt is 45…”

mentioning

confidence: 90%

Separable Schmidt modes of a nonseparable state

et al. 2014

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“…It is worth noting that the counterpropagating geometry allows an easy generation of such a state thanks to the sharply peaked phase-matching versus ω s -ω i . We stress that alternative geometries require more stringent conditions, on either group velocities or other pump properties (extended phase matching (Giovannetti et al, 2002), achromatic phase matching (Torres et al, 2005)). …”

Section: Quantum Properties Of the Two-photon Statementioning

confidence: 99%

Semiconductor Ridge Microcavities Generating Counterpropagating Entangled Photons

Caillet¹,

Orieux²,

Favero³

et al. 2010

Advances in Lasers and Electro Optics

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“…We demonstrated biphoton entanglement in which the two photons have the same frequencies, hence anti-correlated in their times of arrival. By utilizing extended phase-matching [17,18], in which there is zero group-velocity mismatch in the nonlinear crystal, coincident-frequency entanglement was demonstrated in PPKTP under pulsed pumping with a pulse width of 300 fs. This source produced biphotons with 1.3 ps coherence times [19].…”

Section: Sourcesmentioning

confidence: 99%

Quantum Information Technology: Entanglement, Teleportation, and Memory

Shapiro¹

2005

Self Cite

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Public Reporting Burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 The abstract is below since many authors do not follow the 200 V. Giovannetti, S. Lloyd, L. Maccone, and F.N.C. Wong, "Clock synchronization with dispersion cancellation," Phys. Rev. Lett. 87, 117902 (2001).V. Giovannetti, L. Maccone, J.H. Shapiro, and F.N.C. Wong, "Generating entangled two-photon states with coincident frequencies," Phys. Rev. Lett. 88, 183602 (2002).C.E. Kuklewicz, E. Keskiner, F.N.C. Wong, and J.H. Shapiro, "A high-flux entanglement source based on a doubly-resonant optical parametric amplifier," J. Opt. B: Quantum and Semiclass. Opt. 4, S162-S168 ( J. E. Sharping, M. Fiorentino, and P. Kumar, "Observations of twin-beams type quantum correlation in optical fiber," Opt. Lett. 26, 367-369 (2001 X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band," Physical Review Letters 94, 053601 (2005).X. Li, P. L. Voss, J. Chen, K. F. Lee, and P. Kumar, "Measurement of co-and cross-polarized Raman spectra in silica fiber for small detunings," Optics Express, 13, 2236-2244 (2005).X. Li, P. L. Voss, J. Chen, J. E. Sharping, and P. Kumar, "Storage and long-distance distribution of telecommunications-band polarization entanglement generated in an optical fiber," Optics Letters, Vol. 30, No. 10, 2005, pp. 1201-1203 V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, "Classical Capacity of the lossy bosonic channel: the exact solution '', Phys. Rev. Lett. 92, 027902 (2004).S. Lloyd, V. Giovannetti, and L. Maccone, "Physical limits to communication '', Phys. Rev. Lett. 93, 100501 (2004). M. Raginsky, "Almost any quantum spin system with short-range interactions can support toric codes," Phys. Lett. A 294, 153-157 (2002).

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Extended phase-matching conditions for improved entanglement generation

Cited by 79 publications

References 20 publications

Separable Schmidt modes of a nonseparable state

Separable Schmidt modes of a nonseparable state

Semiconductor Ridge Microcavities Generating Counterpropagating Entangled Photons

Quantum Information Technology: Entanglement, Teleportation, and Memory

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