Spatial two-photon coherence of the entangled field produced by down-conversion using a partially spatially coherent pump beam

Jha, Anand K.; Boyd, Robert W.

doi:10.1103/physreva.81.013828

Cited by 48 publications

(52 citation statements)

References 45 publications

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“…We note that in situations in whichγ d (∆τ ′ ) ≈ 1 and κ 1 = κ 2 , the maximum achievable concurrence for a pulsed field can be unity in principle and for a continuous-wave field it can be unity as long as ∆τ is much smaller than the coherence time of the pump field. The above result is the temporal analog of the results obtained in the polarization [31] and spatial [19] degrees of freedom. However, unlike in the spatial degree of freedom, which does not involve any space-averaged detection scheme, the results derived in this article show that even for the time-averaged detection schemes, the temporal correlation properties of the pump do directly decide the upper limit on entanglement that a time-energy entangled two-qubit state can achieve.…”

Section: Rsupporting

confidence: 76%

“…In the polarization degree of freedom it was shown [31] that the degree of polarization P of the pump photon puts an upper bound of (1 + P )/2 on the concurrence of the generated twoqubit state. In the spatial degree of freedom, effects of pump spatial coherence on the entanglement of the generated spatial two-qubit state have been worked out for two-qubit state that have only two non-zero diagonal elements, and for such states it has been shown that the concurrence is bounded by the degree of spatial coherence of the pump field [19]. However, to the best of our knowledge, no such relation has so far been derived for the time-energy entangled two-qubit states.…”

Section: The Special Case Of a Gaussian Schell-model Pump Fieldmentioning

confidence: 99%

“…There have been several studies on how coherence and entanglement properties of the down-converted field are affected by different PDC setting and pump field parameters [17,[24][25][26][27][28][29]. However, regarding how the intrinsic correlations of the pump field get transferred to manifest as two-photon coherence and entanglement, there have been efforts mostly in the polarization and spatial degrees of freedom [19,26,30,31]. In the spatial degree of freedom, a very general spatially partially coherent field was considered and it was shown that the spatial coherence properties of the pump field get entirely transferred to that of the down-converted two-photon field [19].…”

Section: Introductionmentioning

confidence: 99%

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Transfer of temporal coherence in parametric down-conversion

2017

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We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency-bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely-fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statistical information of the pump field. In situations in which the pump is a Gaussian Schell-model field, we derive explicit expressions for the coherence functions. Finally, we show that the concurrence of time-energy-entangled two-qubit states is bounded by the degree of temporal coherence of the pump field. This study can have important implications for understanding how correlations of the pump field manifest as two-particle entanglement as well as for harnessing energy-time entanglement for long-distance quantum communication protocols.Comment: 8 pages, 1 figur

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Section: Rsupporting

confidence: 76%

Section: The Special Case Of a Gaussian Schell-model Pump Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transfer of temporal coherence in parametric down-conversion

2017

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“…Fundamentally, our analysis demonstrates that the lack of momentum correlation does not imply an violation of the conservation of momenta; it shows that the coherence of the pump, i.e. its 'quantumness', is crucial for the generation of entangled photons.A first theoretical analysis [17,18] of the pairgeneration process shows that the angular profile of the pump and its coherence is transferred to the downconverted light. Thus, it determines the uncertainty of the anti-correlation and also effects the generation of entanglement.…”

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confidence: 99%

Influence of pump coherence on the generation of position-momentum entanglement in optical parametric down-conversion

Zhang¹,

Fickler²,

Giese³

et al. 2019

Opt. Express

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Strong correlations in two conjugate variables are the signature of quantum entanglement and have played a key role in the development of modern physics [1,2]. Entangled photons have become a standard tool in quantum information [3] and foundations [4,5]. An impressive example is position-momentum entanglement of photon pairs [6], explained heuristically through the correlations implied by a common birth zone and momentum conservation. However, these arguments entirely neglect the importance of the 'quantumness', i.e. coherence, of the driving force behind the generation mechanism. We study theoretically and experimentally how the correlations depend on the coherence of the pump of nonlinear down-conversion. In the extreme case -a truly incoherent pump -only position correlations exist. By increasing the pump's coherence, correlations in momenta emerge until their strength is sufficient to produce entanglement. Our results shed light on entanglement generation and can be applied to adjust the entanglement for quantum information applications.Entanglement of photons has been explored among different degrees of freedom, such as polarization [4,5,7], time and frequency [8,9], position and momentum [6] as well as angular position and orbital angular momentum [10,11]. Entanglement of two-dimensional systems, in analogy to classical bits, is the primary resource for quantum communication and processing [3]. In addition, multiple-level quantum systems can show highdimensional entanglement with a high complexity [12][13][14] and can be exploited for various quantum information tasks [15]. Position-momentum entanglement as a continuous degree of freedom is the ultimate limit of highdimensional entanglement and its deeper understanding is essential for the development of novel quantum technologies.Position-momentum-entangled photon pairs can be rather straight-forwardly generated in spontaneous parametric down-conversion (SPDC) [6,16], the workhorse of many quantum optics labs. In this process, a strong pump beam spontaneously generates a pair of signal and idler photons through a nonlinear interaction. Formation of position-momentum entanglement is often explained by simple heuristic arguments: A pump photon is converted at one particular transverse position into signal and idler. Due to this common birth place, they are correlated in position. In addition, transverse momentum conservation requires the generated photons to travel in opposite directions, i.e. they are anti-correlated in momentum. Hence, in an idealized situation the generated pairs can be perfectly correlated in both, the position and momenta, which is the key signature of quantum entanglement. However, these arguments have not taken the coherence properties of the pump beam, i.e. the quantum aspect of the driving force behind the pair generation, into account. In this letter, we study how the generation of position-momentum entangled photon pairs relies on the coherence properties of the pump. For that, we pump a nonlinear crystal by a coherent light sour...

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“…In recent years, transfer of the coherence properties of the pump photon to the signal and idler photons has been studied in various different contexts [40,45,46]. In this section, we investigate this transfer in terms of the intrinsic degree of coherence.…”

Section: Transfer Of Intrinsic Degree Of Coherence In Pdcmentioning

confidence: 99%

Intrinsic degree of coherence of two-qubit states and measures of two-particle quantum correlations

Meher¹,

Patoary²,

Kulkarni³

et al. 2020

J. Opt. Soc. Am. B

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Recently, a basis-invariant measure of coherence known as the intrinsic degree of coherence has been established for classical and single-particle quantum states [JOSA B 36, 2765 (2019)]. Using the same mathematical construction, in this article, we define the intrinsic degree of coherence of two-qubit states and demonstrate its usefulness in quantifying two-particle quantum correlations and entanglement. In this context, first of all, we show that the intrinsic degree of coherence of a two-qubit state puts an upper bound on the violations of Bell inequalities that can be achieved with the state and that a two-qubit state with intrinsic degree of coherence less than 1/ √ 3 cannot violate Bell inequalities. We then show that the quantum discord of a two-qubit state, which quantifies the amount of quantum correlations available in the two-qubit state for certain tasks, is bounded from above by the intrinsic degree of coherence of the state. Next, in the context of two-particle entanglement, we show that the range of values that the concurrence of a two-qubit state can take is decided by the intrinsic degree of coherence of the two-qubit state together with that of the individual qubits. Finally, for the polarization two-qubit states generated by parametric down-conversion of a pump photon, we propose an experimental scheme for measuring the intrinsic degree of coherence of two-qubit states. We also present our theoretical study showing how the intrinsic degree of coherence of a pump photon dictates the maximum intrinsic degree of coherence of the generated two-qubit state.

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Spatial two-photon coherence of the entangled field produced by down-conversion using a partially spatially coherent pump beam

Cited by 48 publications

References 45 publications

Transfer of temporal coherence in parametric down-conversion

Transfer of temporal coherence in parametric down-conversion

Influence of pump coherence on the generation of position-momentum entanglement in optical parametric down-conversion

Intrinsic degree of coherence of two-qubit states and measures of two-particle quantum correlations

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