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Chinese Physics B

Einstein-Podolsky-Rosen entanglement in bad cavity case

Yuan Sui-Hong, Xiangming Hu

Published Jul 1, 2010• 2 citations
Publisher

Abstract

This paper explores continuous variable entanglement in four-wave mixing when the atomic relaxation time is comparable to and longer than the cavity relaxation time. In this case the atomic memory is included in the field correlations and the entanglement in the output fields can be significantly enhanced. Einstein–Podolsky–Rosen (EPR) entanglement is achievable even in the bad cavity limit. This shows the EPR entanglement generation without need of good cavity.

DOI
10.1088/1674-1056/19/7/074210

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This paper explores continuous variable entanglement in four-wave mixing when the atomic relaxation time is comparable to and longer than the cavity relaxation time. In this case the atomic memory is included in the field correlations and the entanglement in the output fields can be significantly enhanced. Einstein–Podolsky–Rosen (EPR) entanglement is achievable even in the bad cavity limit. This shows the EPR entanglement generation without need of good cavity.
Atomic memory effects occur when the atomic relaxation times are comparable to or much longer than the cavity relaxation times. We show that by using the memory effects, it is possible to obtain high-frequency Einstein–Podolsky–Rosen entanglement between a pair of Stokes and anti-Stokes fields in a four-wave mixing system. The physical origin is traced to the dynamical Stark splittings of dressed states due to the parametrically amplified fields. This mechanism provides an alternative and efficient way for sideband entanglement.
We explore the effects of atomic memory on quantum correlations of two-mode light fields from four-wave mixing. A three-level atomic system in Λ configuration is considered, in which the atomic relaxation times are comparable to or longer than the cavity relaxation times and thus there exists the atomic memory. The quantum correlation spectrum in the output is calculated without the adiabatic elimination of atomic variables. It is shown that the continuous variable entanglement is enhanced over a wide range of the normalized detuning in the intermediate and bad cavity cases compared with the good cavity case. In some situations more significant enhancement occurs at sidebands.
Summary form only given. With the rapid development of spatially-resolving single-photon detectors, spatially structured multidimensional entangled states start to play a key role in modern quantum science. In particular, they find extensive applications in emerging fields such as quantum imaging, holography, computation or quantum-enhanced metrology. Moreover, spatially-multiplexed schemes hold a promise to increase the capacity of quantum channels, essential for quantum key distribution. An appealing perspective is to apply these ideas to light-atom interfaces, that are capable of storing and processing continuous-variable (CV) entanglement, critical for novel quantum cryptography, computation and imaging schemes.Here we generate a hybrid bipartite entangled state of a photon and an atomic spin-wave excitation [1], exhibiting Einstein-Podolsky-Rosen (EPR) correlations in real space of continuous position-momentum variables, as in the original EPR proposal [2]. We verify the entanglement by measuring the coincidence patterns corresponding to modulus-squared spatial wavefunctions of the state. By studying temporal evolution and decoherence we find that the EPR entanglement may be stored for several microseconds. Our approach turns out to be by far more robust than the only hitherto performed experiment, based on quadratures of squeezed light and a slow-light medium, where time-delayed EPR correlations were demonstrated [3]. We achieve two orders of magnitude longer delay time using quantum memory setup and significantly stronger violation of EPR inequality [4], with product of variances 3 times below the EPR bound for the full two-dimensional coincidence distribution.
Abstract We investigate theoretically quantum entanglement of light with the collective spin polarization of a cold atomic ensemble in cavity-assisted Raman schemes. Previous works concentrated mostly on the bad cavity limit where the signals are much longer than the cavity field lifetime. In view of atomic relaxation and other imperfections, there may arise a need to speed-up the light-atoms interface operation. By increasing the cavity field lifetime, one can achieve better light–matter coupling and entanglement. In our work, we consider the non-adiabatic effects that become important beyond the bad cavity limit in both low-photon and continuous variables regime. We find classical control field time profiles that allow one to retrieve from the cavity an output quantized signal of a predefined time shape and duration, which is optimal for the homodyne detection, optical mixing or further manipulation. This is done for a wide range of the signal duration as compared to the cavity field lifetime. We discuss an optimal cavity–atomic ensemble matching in terms of the cavity field lifetime which allows one to apply less intense control field and to minimize a variety of nonlinear effects, such as AC light shifts, four-wave mixing, etc, which may be potentially harmful to an experiment.
We present a collection of our recent schemes that have been proposed for continuous variable entanglement. Included in this collection are two types of optical systems. One is the four-wave mixing in resonantly or near-resonantly driven atomic systems. The numerical results and physical analyses are presented by using dressed atomic states and squeeze transformed cavity modes. Two dissipation channels are identified, through which the dressed atoms simultaneously absorb in the excitations from the pair of squeeze transformed modes. It is in the presence of such two channels that the entanglement is greatly enhanced and the best achievable state is the original Einstein-Podolsky-Rosen (EPR) entangled state. This scheme is applicable in the optical regime where atomic spontaneous emission has to be taken into account, unlike the two-step atomic reservoir engineering scheme, which is limited to the microwave regime. The other kind of systems is the quantum-beat laser with incoherent pump or coherent driving. Such a laser, when it operates well above threshold, produces entangled light. The numerical results and physical analyses are presented by using the collective modes of the lasing fields. The relative mode is decoupled from the active medium and thus remains in its vacuum state, while the sum mode operates well above threshold and displays sub-shot noise. The quantum-beat and the sum mode intensity noise reduction combine to yield entanglement between two bright beams and sub-Poissonian photon statistics of respective beams.
Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low-resource generation of bipartite continuous-variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e., the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than 33.333.333.3 %. However, arbitrarily strong EPR entanglement is generally possible with this scheme. We realize continuous-wave squeezed light at 155015501550 nm with up to 9.99.99.9 dB of nonclassical noise reduction, which is the highest value at a telecom wavelength so far. Using two phase-controlled balanced homodyne detectors we observe an EPR covariance product of $0.502\ifmmode\pm\else\textpm\fi{}0.006<1$, where 111 is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network.