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arXiv:1510.01021 · Physical Review A

Entangled collective-spin states of atomic ensembles under nonuniform atom-light interaction

Jiazhong Hu, Wenlan Chen, Zachary Vendeiro, Hao Zhang, Vladan Vuletić

Published Dec 9, 2015• 40 citations
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Abstract

We consider the optical generation and characterization of entanglement in atomic ensembles under nonuniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of nonuniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the average total spin remains large, and the detection does not resolve single spins. Furthermore, we derive an analytic formula for determining the observable entanglement in the case, of relevance in practice, where the ensemble-mode coupling differs between state generation and measurement.

DOI
10.1103/physreva.92.063816

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We consider the optical generation and characterization of entanglement in atomic ensembles under nonuniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of nonuniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the average total spin remains large, and the detection does not resolve single spins. Furthermore, we derive an analytic formula for determining the observable entanglement in the case, of relevance in practice, where the ensemble-mode coupling differs between state generation and measurement.
The interaction between an atomic ensemble and a light mode in a high-finesse optical cavity can easily reach the strong-coupling regime, where quantum effects dominate.In this regime, the interaction can be used to generate both atom-light and atom-atom entanglement.We analyze the dominant effects on the collective atomic state and the light field, and derive a unified approach that can account for atomic entanglement induced both by measurements on the light field, and by ignoring the state of the light field altogether.We present analytical expressions for the entanglement induced by the interaction, and determine the conditions that maximize the entanglement-induced gain over the standard quantum limit in quantum sensors and atomic clocks.
We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or multifrequency light, the atom-light interaction entangles the frequency spectrum of a transmitted photon with the collective spin of the atomic ensemble. Simple time-resolved detection of the transmitted photon then projects the atomic ensemble into a desired pure entangled state. This method can be implemented with existing technology, yields high success probability per trial, and can generate complex entangled states such as mesoscopic superposition states of coherent spin states with high fidelity.
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.
In this thesis, we explore the quantum dynamics of light interactions with optically thick collections of atoms. We provide a theoretical description of several recent experiments in which some key operations necessary for the implementation of quantum communication networks are demonstrated. Collective Raman scattering from an atomic ensemble is shown to produce probabilistic entanglement between the polarization of a scattered photon and an associated collective atomic excitation. The predicted correlations agree with experimental observations. We also propose a method to use cascade transitions to produce entanglement between a photon with a frequency in the telecom range (ideal for transmission over optical fibers) and a near infrared photon (ideal for storage in an atomic ensemble), and a description of the experimental demonstration is provided. We also propose and describe the implementation of a deterministic source of single photons.\n\nIn addition, we generalize the theory of dark-state polaritons in ensembles of three level Lambda atoms to account for the nuclear spin degeneracy of alkali atoms. This generalized theory provides a description of the first demonstration of single photon storage and retrieval from atomic ensembles. Additionally, in the presence of a uniform magnetic field, we predict the occurrence of collapses and revivals of the photon retrieval efficiency as a function of storage time within the ensemble. These predictions are in very good agreement with subsequent experimental observations. We also exploit the ability of photon storage to entangle remote atomic qubits.
Summary form only given. A new approach to the problem of the quantum interface between light and atoms has been recently developed. The method utilizes free space dispersive interaction between pulses of light and spin polarized atomic ensembles. Entanglement between the polarization state of light and the collective spin state of atoms is established by measurement, more precisely by detection of light in a certain polarization basis. In the first demonstration of this approach we have generated a long-lived entangled state of two separate macroscopic atomic samples by a polarization measurement on light transmitted through the samples. We then have shown that this approach also works for mapping of a quantum state of light onto long-lived atomic spin state paving the road towards realization of the quantum memory for light. Recently we have also extended the free space light-atoms interface beyond the continuous variables in the proposal, where a coherent superposition "cat" state of an atomic ensemble is generated by a measurement sequence. Progress with other communication protocols such as atomic state teleportation and multiparty networks will be presented.
Entanglement generation between atomic ensembles is typically modeled using the framework of continuous variables (CV) which approximates discrete spin operators as canonical position and momentum operators. Although hugely successful with many applications, this approximation is valid only for small deviations in spin. Here we investigate entanglement generation between two atomic ensemble qubits using a measurement based scheme of a common light mode. Various methods of entanglement detection of the entangled state is discussed. We propose a entanglement witness for this state and discuss its further applications to optical states.