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Two-mode squeezing in a cold atomic ensemble

Arina Tashchilina

Published Nov 1, 2019• 1 citation
Publisher

Abstract

We investigate experimentally and theoretically the generation of a continuous variable entanglement using laser cooled atomic gas in free space and cavity mode. This is of a fundamental interest due to the nonclassical correlation of quadrature observables of the two-mode squeezed (TMS) state. The TMS state is the basis for complete quantum teleportation and continuous variable quantum repeaters. It is also used in quantum metrology and quantum key distribution. We employ a novel scheme for generating a TMS vacuum based on a non-degenerate four-wave mixing process in a cold atomic cloud coupled to a cavity. We send two pumps collinear to the cavity mode and ensure that the two generated quantum fields are simultaneously resonant with the cavity. The cavity enhancement enables us to demonstrate results close to a free space in hot atomic gases (-5.2 dB) where optical densities are much higher. Our system is versatile because, together with continuous variables, it is suitable for the discrete variable domain using the Duan-Lukin-Cirac-Zoller protocol. The design is oriented to make the delay between two modes possible and could be used for hybrid continuous repeaters. The system is devised and built fully as a part of my PhD, wherein we characterize our system and demonstrate the squeezing of -3.7 dB. Since the quantum dynamics of the system is not intuitive, we provide simple models and consolidate segmental information on generation of TMS states. To make sure that the dynamics is not oversimplified, we construct a novel theory where we treat both fields and atoms as quantum objects. The theory supports and enriches our understanding and confirms our experimental data. Based on the experimental and theoretical results we spotlight the detrimental effects and propose improvements to our system. We theoretically investigate that the certain class of TMSV states are optically dark. These states propagate through a polarized to one hyperfine level Λ atoms without degradation or evolution. Based on this we propose a new way of generation of TMSV through the dissipation or dynamically controlled broadening.

DOI
10.11575/prism/37285

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We investigate experimentally and theoretically the generation of a continuous variable entanglement using laser cooled atomic gas in free space and cavity mode. This is of a fundamental interest due to the nonclassical correlation of quadrature observables of the two-mode squeezed (TMS) state. The TMS state is the basis for complete quantum teleportation and continuous variable quantum repeaters. It is also used in quantum metrology and quantum key distribution. We employ a novel scheme for generating a TMS vacuum based on a non-degenerate four-wave mixing process in a cold atomic cloud coupled to a cavity. We send two pumps collinear to the cavity mode and ensure that the two generated quantum fields are simultaneously resonant with the cavity. The cavity enhancement enables us to demonstrate results close to a free space in hot atomic gases (-5.2 dB) where optical densities are much higher. Our system is versatile because, together with continuous variables, it is suitable for the discrete variable domain using the Duan-Lukin-Cirac-Zoller protocol. The design is oriented to make the delay between two modes possible and could be used for hybrid continuous repeaters. The system is devised and built fully as a part of my PhD, wherein we characterize our system and demonstrate the squeezing of -3.7 dB. Since the quantum dynamics of the system is not intuitive, we provide simple models and consolidate segmental information on generation of TMS states. To make sure that the dynamics is not oversimplified, we construct a novel theory where we treat both fields and atoms as quantum objects. The theory supports and enriches our understanding and confirms our experimental data. Based on the experimental and theoretical results we spotlight the detrimental effects and propose improvements to our system. We theoretically investigate that the certain class of TMSV states are optically dark. These states propagate through a polarized to one hyperfine level Λ atoms without degradation or evolution. Based on this we propose a new way of generation of TMSV through the dissipation or dynamically controlled broadening.
We report on the generation of non-separable beams produced via the interaction of a linearly polarized beam with a cloud of cold caesium atoms placed in an optical cavity. We convert the squeezing of the two linear polarization modes into quadrature entanglement and show how to find the best entanglement generated in a two-mode system using the inseparability criterion for continuous variables (Duan et al 2000 Phys. Rev. Lett. 84 2722). We verify this method experimentally with a direct measurement of the inseparability using two homodyne detectors. We then map this entanglement into a polarization basis and achieve polarization entanglement .
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of non-commuting observables between two subsystems. At the same time, these subsystems themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental dephasing process of quantum cross-correlations in continuous-variable propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain the insight into finite-time entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of non-commuting observables between two subsystems. At the same time, these subsystems themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental dephasing process of quantum cross-correlations in continuous-variable propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain the insight into finite-time entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.
The generation of entanglement in atomic systems plays a central topic in the fields of quantum information storage and processing. Moreover, a special category of entangled states of multi-atom ensembles, spin squeezed states, have been proven to lead to considerable improvement in the sensitivity of precision measurements compared to systems involving uncorrelated atoms. A treatment of entanglement in open systems is, however, incomplete without a precise description of the process of decoherence which necessarily accompanies it. The theory of entanglement and decoherence are the two main topics of this thesis. Methods are described for the generation of strong correlations in large atomic ensembles using either cavity quantum electrodynamics or measurement outcome conditioned quantum dynamics. Moreover, the description of loss of entanglement resulting from the coupling to a noise reservoir (electromagnetic vacuum) is explored. A spin squeezing parameter is used throughout this thesis as both a measure of entanglement strength and as an indication of the sensitivity improvement above the so-called standard quantum limit (sensitivity obtained with uncorrelated particles) in metrology. The first scheme considered consists of a single mode cavity field interacting with a collection of atoms for which spin squeezing is produced in both resonant and off-resonant regimes. In the resonant case, transfer of squeezing from a field state to the atoms is analyzed, while in the off-resonant regime squeezing is produced via an effective nonlinear interaction (one-axis twisting Hamiltonian). A second, more experimentally realistic case, is one involving the interaction of free space atoms with laser pulses; a projective measurement of a source field originating from atomic fluctuations provides a means of preparing atomic collective states such as spin squeezed and Schrodinger cat states. A new unravelling is proposed, that employs the detection of photon number in a single output channel and is capable of producing mesoscopic Schrodinger cat states in a single step. As a first step to understanding the role of cooperative decoherence, of importance in the case of dense pencil-shaped atomic ensembles, the collective spin decoherence of a two multilevel atom system is derived. This calculation is also relevant to entanglement loss for two qubits manipulated using with reading/writing pulses. Finally, a scheme is proposed in which arbitrarily strong entanglement can be produced in a four-wave mixing setup, where the preparation of the atoms in a dark state limits the decoherence to negligible values.
Future quantum repeater architectures, capable of efficiently distributing information encoded in quantum states of light over large distances, will benefit from multiplexed photonic quantum memories. In this work we demonstrate a temporally multiplexed quantum repeater node in a laser-cooled cloud of ^{87}Rb atoms. We employ the Duan-Lukin-Cirac-Zoller protocol where pairs of photons and single collective spin excitations (so-called spin waves) are created in several temporal modes using a train of write pulses. To make the spin waves created in different temporal modes distinguishable and enable selective readout, we control the dephasing and rephasing of the spin waves by a magnetic field gradient, which induces a controlled reversible inhomogeneous broadening of the involved atomic hyperfine levels. We demonstrate that by embedding the atomic ensemble inside a low finesse optical cavity, the additional noise generated in multimode operation is strongly suppressed. By employing feed forward readout, we demonstrate distinguishable retrieval of up to 10 temporal modes. For each mode, we prove nonclassical correlations between the first and second photon. Furthermore, an enhancement in rates of correlated photon pairs is observed as we increase the number of temporal modes stored in the memory. The reported capability is a key element of a quantum repeater architecture based on multiplexed quantum memories.
We present an experimental demonstration of both quadrature and polarization entanglement generated via the interaction between a coherent linearly polarized field and cold atoms in a high finesse optical cavity. The nonlinear atom-field interaction produces two squeezed modes with orthogonal polarizations which are used to generate a pair of nonseparable beams, the entanglement of which is demonstrated by checking the inseparability criterion for continuous variables recently derived by Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)]] and calculating the entanglement of formation [Phys. Rev. Lett. 91, 107901 (2003)]].