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Physical Review A

Sensitive detection of entanglement in exciton-polariton condensates via spin squeezing

Jingyan Feng, Ebubechukwu O. Ilo-Okeke, Alexey N. Pyrkov, Alexis Askitopoulos, Tim Byrnes

Published Jul 30, 2021• 9 citations
Publisher

Abstract

We propose a method of generating and detecting entanglement via spin squeezing in an exciton-polariton condensate. Spin squeezing is a sensitive detector of entanglement because any squeezing below shot noise implies entanglement. In our scheme, two polariton spin species are resonantly pumped, forming a particle number fluctuating effective spin. The naturally occurring nonlinear interactions between the polaritons produce an effective one-axis squeezing interaction, which drives the system toward a spin-squeezed state at steady-state. We investigate the squeezing level that is attainable at the steady state for realistic experimental parameters and show the favorable parameters for strong squeezing. The amount of squeezing tends to improve with larger pumping, due to the bosonic enhancement of the one-axis twisting Hamiltonian. Using number-fluctuating versions of the Wineland squeezing criterion and optimal spin inequalities, we show how multipartite entanglement can be detected.

DOI
10.1103/physreva.104.013318

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We propose a method of generating and detecting entanglement via spin squeezing in an exciton-polariton condensate. Spin squeezing is a sensitive detector of entanglement because any squeezing below shot noise implies entanglement. In our scheme, two polariton spin species are resonantly pumped, forming a particle number fluctuating effective spin. The naturally occurring nonlinear interactions between the polaritons produce an effective one-axis squeezing interaction, which drives the system toward a spin-squeezed state at steady-state. We investigate the squeezing level that is attainable at the steady state for realistic experimental parameters and show the favorable parameters for strong squeezing. The amount of squeezing tends to improve with larger pumping, due to the bosonic enhancement of the one-axis twisting Hamiltonian. Using number-fluctuating versions of the Wineland squeezing criterion and optimal spin inequalities, we show how multipartite entanglement can be detected.
We propose a method of generating and detecting spatially defined entanglement in exciton-polariton condensates at steady state. In our scheme we first create a spinor polariton condensate, such that steady-state squeezing is obtained under a one-axis twisting interaction. Then the condensate is split either physically or virtually, which results in entanglement generated between the two parts. A virtual split means that the condensate is not physically split, but its near-field image is divided into two parts, and the spin correlations are deduced from polarization measurements in each half. We theoretically model and examine the logarithmic negativity criterion and several correlation-based criteria to show that entanglement exists under experimentally achievable parameters.
This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to SU(2) rotations, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin-squeezed states produced with nonlinear twisting Hamiltonians. Afterwards, we explain pairwise correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the latter plays a central role in quantum metrology. We also review the applications of spin squeezing for detecting quantum chaos and quantum phase transitions, as well as the influence of decoherence on spin squeezing. Finally, we review several experimental realizations of spin squeezing, as well as their corresponding theoretical backgrounds, including: producing spin-squeezed states via particle collisions in Bose-Einstein condensates, transferring photon squeezing to atomic ensembles, and generating spin squeezing via quantum non-demolition measurements.
We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits greater than 1 or via the two-axis countertwisting Hamiltonian for any even number of qubits, the numerical results suggest that such states are spin squeezed if and only if they are pairwise entangled.
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.
Squeezed spin states possess unique quantum correlation or entanglement and are significantly promising for advancing quantum information processing and quantum metrology. In recent back-to-back publications [C. Gross et al., Nature (London) 464, 1165 (2010) and Max F. Riedel et al., Nature (London) 464, 1170 (2010)], reduced spin fluctuations are observed leading to spin squeezing at -8.2 and -2.5 dB, respectively, in two-component atomic condensates exhibiting one-axis-twisting interactions. The noise reduction limit for the one-axis twisting scales as ∝1/N(2/3), which for a condensate with N∼10(3) atoms is about 100 times below the standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the one-axis-twisting spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction ∝1/N or an extra tenfold improvement for N∼10(3).