We theoretically discuss the preservation of squeezing and continuous variable entanglement of two mode squeezed light when the two modes are subjected to unequal transmission. One of the modes is transmitted through a slow light medium while the other is sent through an optical fiber of unit transmission. Balanced homodyne detection is used to check the presence of squeezing. It is found that loss of squeezing occurs when the mismatch in the transmission of the two modes is greater than 40% while near ideal squeezing is preserved when the transmissions are equal. We also discuss the effect of this loss on continuous variable entanglement using strong and weak EPR criteria and possible applications for this experimental scheme.
This work analyses the quantum properties of counter-propagating twin beams generated by a Mirrorless Optical Parametric Oscillator in the continuous variable regime. Despite the lack of the filtering effect of a cavity, we show that in the vicinity of its threshold it may generate high levels of narrowband squeezing and Einstein-Podolsky-Rosen (EPR) correlation, completely comparable to what can be obtained in standard optical parametric oscillators.
We report on the experimental demonstration of strong quadrature EPR entanglement and squeezing at very low noise sideband frequencies produced by a single type-II, self-phase-locked, frequency degenerate optical parametric oscillator below threshold. The generated two-mode squeezed vacuum state is preserved for noise frequencies as low as 50 kHz. Designing simple setups able to generate non-classical states of light in the kHz regime is a key challenge for high sensitivity detection of ultra-weak physical effects such as gravitational wave or small beam displacement.
We show how one can prepare and detect entanglement and Einstein-Podolsky-Rosen (EPR) steering between two distinguishable groups (modes) of atoms in a Bose-Einstein condensate (BEC) atom interferometer. Our paper extends previous work that developed criteria for two-mode entanglement and EPR steering based on the reduced variances of two spins defined in a plane. Observation of planar spin squeezing will imply entanglement, and sufficient planar spin squeezing implies EPR steering, between the two groups of atoms. By using a two-mode dynamical model to describe BEC interferometry experiments,…
We present the experimental realization of a theoretical effect discovered by Olivares and Paris, in which a pair of entangled optical beams undergoing independent losses can see nonlocal correlations restored by the use of a nonlocal resource correlating the losses. Twin optical beams created in an entangled Einstein-Podolsky-Rosen (EPR) state by an optical parametric oscillator above threshold were subjected to 50% loss from beamsplitters in their paths. The resulting severe degradation of the signature quantum correlations observed between the two beams was then suppressed when another, ind…
Based on total variance of a pair of Einstein-Podolsky-Rosen (EPR) type operators, the generalized EPR entangled states in continuous variable systems are defined. We show that such entangled states must correspond with two-mode squeezing states whether these states are Gaussian or not and whether they are pure or not. With help of the relation between the total variance and the entanglement, the degree of such entanglement is also defined. Through analyzing some specific cases, we see that this method is very convenient and easy in practical application. In addition, an entangled state with n…
We propose and analyze a scheme to entangle the collective spin states of two spatially separated bimodal Bose-Einstein condensates. Using a four-mode approximation for the atomic field, we show that elastic collisions in a state-dependent potential simultaneously create spin-squeezing in each condensate and entangle the collective spins of the two condensates. We investigate mostly analytically the non-local quantum correlations that arise in this system at short times and show that Einstein-Podolsky-Rosen (EPR) entanglement is generated between the condensates. At long times we point out mac…
Broadband quantum noise reduction can be achieved in gravitational wave detectors by injecting frequency dependent squeezed light into the the dark port of the interferometer. This frequency dependent squeezing can be generated by combining squeezed light with external filter cavities. However, in future long baseline interferometers (LBIs), the filter cavity required to achieve the broadband squeezing has a low bandwidth -- necessitating a very long cavity to mitigate the issue from optical loss. It has been shown recently that by taking advantage of Einstein-Podolsky-Rosen (EPR) entanglement…
The Standard Quantum Limit (SQL) in interferometric displacement measurement imposes a restriction on the precision of the measurement due to its quantum back-action noise. This limit can be surpassed over a broad frequency band by injecting squeezed vacuum states with a frequency dependent (FD) quadrature angle into the measurement system. Here, we demonstrate the generation of FD squeezed vacuum states by utilizing Einstein-Podolsky-Rosen (EPR) entangled states. The frequency dependence of the squeezed state can be tuned by conditionally filtering the measurement once the two entangled field…
We investigate the spatial quantum properties of the light emitted by a perfectly spatially degenerate optical parametric oscillator (self-imaging OPO). We show that this device produces local squeezing for areas bigger than a coherence are that depends on the crystal length and pump width. Furthermore, it generates local EPR beams in the far field. We show, calculating the eigenmodes of the system, that it is highly multimode for realistic experimental parameters.
The Stokes and anti-Stokes components of the spectrum of resonance fluorescence of a single trapped atom, which originate from the mechanical coupling between the scattered photons and the quantized motion of the atomic center of mass, exhibit quantum correlations which are of two-mode-squeezing type. We study and demonstrate the build-up of such correlations in a specific setup, which is experimentally accessible, and where the atom acts as efficient and continuous source of EPR-entangled, two-mode squeezed light.
We show how to generate bilinear (quadratic) Hamiltonians in cavity quantum electrodynamics (QED) through the interaction of a single driven three-level atom with two (one) cavity modes. With this scheme it is possible to generate one-mode mesoscopic squeezed superpositions, two-mode entanglements, and two-mode squeezed vacuum states (such the original EPR state), without the need for Ramsey zones and external parametric amplification. The degree of squeezing achieved is up to 99% with currently feasible experimental parameters and the errors due to dissipative mechanisms become practically ne…
We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced…
In a previous paper tests for entanglement for two mode systems involving identical massive bosons were obtained. In the present paper we consider sufficiency tests for EPR steering in such systems. We find that spin squeezing in any spin component, a Bloch vector test, the Hillery-Zubairy planar spin variance test and squeezing in two mode quadratures all show that the quantum state is EPR steerable. We also find a generalisation of the Hillery-Zubairy planar spin variance test for EPR steering. The relation to previous correlation tests is discussed. This paper is based on a detailed classif…
A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of …
We demonstrate the applicability of the EPR entanglement squeezing scheme for enhancing the shot-noise-limited sensitivity of a detuned dual-recycled Michelson interferometers. In particular, this scheme is applied to the GEO\,600 interferometer. The effect of losses throughout the interferometer, arm length asymmetries, and imperfect separation of the signal and idler beams are considered.
We have experimentally realized the scheme initially proposed as quantum dense coding with continuous variables [Ban, J. Opt. B \textbf{1}, L9 (1999), and Braunstein and Kimble, \pra\textbf{61}, 042302 (2000)]. In our experiment, a pair of EPR (Einstein-Podolski-Rosen) beams is generated from two independent squeezed vacua. After adding two-quadrature signal to one of the EPR beams, two squeezed beams that contain the signal were recovered. Although our squeezing level is not sufficient to demonstrate the channel capacity gain over the Holevo limit of a single-mode channel without entanglement…
We report the suitability of an Einstein-Podolsky-Rosen (EPR) entanglement source for gaussian continuous-variable quantum key distribution at 1550 nm. Our source is based on a single continuous-wave squeezed vacuum mode combined with a vacuum mode at a balanced beam splitter. Extending a recent security proof, we characterize the source by quantifying the extractable length of a composable secure key from a finite number of samples under the assumption of collective attacks. We show that distances in the order of 10 km are achievable with this source for a reasonable sample size despite the f…
We propose to generate Einstein-Podolsky-Rosen (EPR) entanglement between groups of atoms in a two-well Bose-Einstein condensate using a dynamical process similar to that employed in quantum optics. The local nonlinear S-wave scattering interaction has the effect of creating a spin squeezing at each well, while the tunneling, analogous to a beam splitter in optics, introduces an interference between these fields that results in an inter-well entanglement. We consider two internal modes at each well, so that the entanglement can be detected by measuring a reduction in the variances of the sums …
This Colloquium examines the field of the EPR Gedankenexperiment, from the original paper of Einstein, Podolsky and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. We analyze the relationship with entanglement and Bell's theorem, and summarize the progress to date towards experimental confirmation of the EPR paradox, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fibre quantum soli…
We report on the generation of a continuous variable Einstein-Podolsky-Rosen (EPR) entanglement using an optical fibre interferometer. The Kerr nonlinearity in the fibre is exploited for the generation of two independent squeezed beams. These interfere at a beam splitter and EPR entanglement is obtained between the output beams. The correlation of the amplitude (phase) quadratures are measured to be 4.0+-0.2 (4.0+-0.4) dB below the quantum noise limit. The sum criterion for these squeezing variances 0.80+-0.03 < 2 verifies the nonseparability of the state. The product of the inferred uncertain…
Einstein, Podolsky & Rosen (EPR) pointed out that correlations induced between quantum objects will persist after these objects have ceased to interact. Consequently, their joint continuous variables (CV), e.g., the difference of their positions and the sum of their momenta, may be specified, regardless of their distance, with arbitrary precision. EPR correlations give rise to two fundamental notions: {\em nonlocal ``steering''} of the quantum state of one object by measuring the other, and inseparability ({\em entanglement}) of their quantum states. EPR entanglement is a resource of quantum i…
The Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a ligh…
Multi-component correlation functions are developed by utilizing d-outcome measurements. Based on the multi-component correlation functions, we propose a Bell inequality for bipartite d-dimensional systems. Violation of the Bell inequality for continuous variable (CV) systems is investigated. The violation of the original Einstein-Podolsky-Rosen state can exceed the Cirel'son bound, the maximal violation is 2.96981. For finite value of squeezing parameter, violation strength of CV states increases with dimension d. Numerical results show that the violation strength of CV states with finite squ…
We propose a scheme for continuous-variable telecloning with phase-conjugate inputs (PCI). Two cases of PCI telecloning are considered. The first case is where PCI telecloning produces $M$ clones nonlocally and $M$ anticlones locally, or vice versa. This kind of PCI telecloning requires only one EPR (Einstein-Podolsky-Rosen) entangled, two-mode squeezed state as a resource for building the appropriate multi-mode, multipartite entangled state via linear optics. The other case is a PCI telecloning protocol in which both clones and anticlones are created nonlocally. Such a scheme requires two EPR…
Encoding quantum information in continuous variables (CV)---as the quadrature of electromagnetic fields---is a powerful approach to quantum information science and technology. CV entanglement---light beams in Einstein-Podolsky-Rosen (EPR) states---is a key resource for quantum information protocols; and enables hybridisation between CV and single photon discrete variable (DV) qubit systems. However, CV systems are currently limited by their implementation in free-space optical networks: increased complexity, low loss, high-precision alignment and stability, as well as hybridisation, demand an …
We propose a scheme for generating two-mode squeezing in high-Q resonators using a beam of atoms with random arrival times, which acts as a reservoir for the field. The scheme is based on four-wave mixing processes leading to emission into two cavity modes, which are resonant with the Rabi sidebands of the atomic dipole transition, driven by a saturating classical field. At steady state the cavity modes are in an Einstein-Podolski-Rosen (EPR) state, whose degree of entanglement is controlled by the intensity and the frequency of the transverse field. This scheme is robust against stochastic fl…
We investigate how the entanglement properties of a two-mode state can be improved by performing a coherent superposition operation of photon subtraction and addition, proposed by Lee and Nha [Phys. Rev. A 82, 053812 (2010)], on each mode. We show that the degree of entanglement, the EPR-type correlation, and the performance of quantum teleportation can be all enhanced for the output state when the coherent operation is applied to a two-mode squeezed state. The effects of the coherent operation are more prominent than those of the mere photon subtraction and the addition particularly in the sm…
We show that non-classical intensity correlations and quadrature entanglement can be generated by frequency doubling in a resonator with two output ports. We predict twin-beam intensity correlations 6 dB below the coherent state limit, and that the product of the inference variances of the quadrature fluctuations gives an Einstein-Podolsky-Rosen (EPR) correlation coefficient of V_EPR = 0.6 < 1. Comparison with an entanglement source based on combining two frequency doublers with a beam splitter shows that the dual ported resonator provides stronger entanglement at lower levels of individual be…
Dynamics of entangled states of two independent single-mode cavities in squeezed reservoirs is investigated in the context of matching of the correlations contained in the entangled states to those contained in the squeezed reservoir. We illustrate our considerations by examining the time evolution of entanglement of single and double excitation NOON and EPR states. A comparison is made when each cavity is coupled to own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservo…
In their seminal paper, Caves and Schumaker presented a new formalism for quantum optics, intended to serve as a building block for describing two-photon processes, in terms of new, generalized qudratures. The important, revolutionary concept in their formalism was that it was fundamentally two-mode, i.e. the related observables could not be attributed to any single one of the comprising modes, but rather to a generalized complex quadrature that could only be attributed to both of them. Here, we propose a subtle, but fundamentally meaningful modification to their important work. Unlike the abo…
We consider tripartite entangled states for continuous variable systems of EPR type, which generalise the famous bipartite CV EPR states (eigenvectors of conjugate choices X1 - X2, P1+ P2, of the systems' relative position and total momentum variables). We give the regularised forms of such tripartite EPR states in second-quantised formulation, and derive their Wigner functions. This is directly compared with the established NOPA-like states from quantum optics. Whereas the multipartite entangled states of NOPA type have singular Wigner functions in the limit of large squeezing, r --> infinity…
In this paper, we propose a continuous measurement and feedback scheme to achieve strong Einstein-Podolsky-Rosen (EPR) steering and Bell nonlocality of two macroscopic mechanical oscillators in cavity optomechanics. Our system consists of two optomechanical cavities in which two cavity fields are coupled to each other via a nondegenerate parametric downconversion. The two cavity output fields are subject to continuous Bell-like homodyne detection and the detection currents are fed back to drive the cavity fields. It is found that when the feedback is absent, the two mechanical oscillators can …
We report the realization of a bright ultrafast two-mode squeezer based on type II parametric downconversion (PDC) in periodically poled $\mathrm{KTiOPO_4}$ (PP-KTP) waveguides. It produces a pulsed two-mode squeezed vacuum state: a photon-number entangled pair of truly single-mode pulses or, in terms of continuous variables quantum optics, a pulsed, single mode Einstein-Podolsky-Rosen (EPR) state in the telecom regime. We prove the single mode character of our source by measuring its $g^{(2)}$ correlation function and demonstrate a mean photon number of up to 2.5 per pulse, equivalent to 11dB…
The need for high fidelity quantum teleportation arises in a variety of quantum algorithms and protocols. Unfortunately, conventional continuous variable teleportation schemes rely on EPR states that yield a fidelity that approaches unity only in the limit of an unphysical amount of squeezing. A new method, which utilizes an ensemble of single photon entangled states to teleport continuous variable states with fidelity approaching unity with finite resources was recently proposed by Andersen and Ralph [Phys. Rev. Lett. 111, 050504 (2013)]. We extend these ideas to consider the general case of …
Quantum Steering and Entanglement in a Tritter: Hierarchy under Loss
College of Electronic and Information Engineering, Nanchang Institute of Technology（南昌工程学院电子信息工程学院）；Center for Quantum Science and Technology, Jiangxi Normal University（江西师范大学量子科学与技术中心）；Institute for Military-Civilian Integration of Jiangxi Province（江西省军民融合研究院）；School of Photoelectric Engineering, Jiangxi Modern Polytechnic College（江西现代职业技术学院光电工程学院）
A quantum memory for light is a key element for the realization of future quantum information networks. Requirements for a good quantum memory are (i) versatility (allowing a wide range of inputs) and (ii) true quantum coherence (preserving quantum information). Here we demonstrate such a quantum memory for states possessing Einstein-Podolsky-Rosen (EPR) entanglement. These multi-photon states are two-mode squeezed by 6.0 dB with a variable orientation of squeezing and displaced by a few vacuum units. This range encompasses typical input alphabets for a continuous variable quantum information …
Proposals for solid state quantum computing are extremely promising as they can be used to built room temperature quantum computers. If such a quantum computer is ever built it would require in-built sources of nonclassical states required for various quantum information processing tasks. Possibilities of generation of such nonclassical states are investigated here for a physical system composed of a monochromatic light coupled to a two-band semiconductor with direct band gap. The model Hamiltonian includes both photon-exciton and exciton-exciton interactions. Time evolution of the relevant bo…
