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arXiv:quant-ph/0603197 · Physical Review Letters

Spin Squeezing and Light Entanglement in Coherent Population Trapping

Aurélien Dantan, J. Cviklinski, E. Giacobino, M. Pinard

Published Jul 14, 2006• 68 citations
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Abstract

We show that strong squeezing and entanglement can be generated at the output of a cavity containing atoms interacting with two fields in a coherent population trapping situation, on account of a nonlinear Faraday effect experienced by the fields close to a dark-state resonance in a cavity. Moreover, the cavity provides a feedback mechanism allowing to reduce the quantum fluctuations of the ground state spin, resulting in strong steady state spin squeezing.

DOI
10.1103/physrevlett.97.023605

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•Jan 1, 2006•0 citations
We show that strong squeezing and entanglement can be generated at the output of a cavity containing atoms interacting with two fields in a coherent population trapping situation, on account of a nonlinear Faraday effect experienced by the fields close to a dark-state resonance in a cavity. Moreover, the cavity provides a feedback mechanism allowing to reduce the quantum fluctuations of the ground state spin, resulting in strong steady state spin squeezing.
Spin squeezing has important applications in the field of quantum metrology and quantum information processing. Here we propose that coherent population trapping is well suitable for establishing cavity dissipation mechanism and generating a spin-squeezed state. An ensemble of N double Λ -type atoms is placed inside the two-mode optical cavity, where one Λ subsystem is driven resonantly by two strong control fields to form a dark resonance and the other Λ subsystem is coupled by two cavity vacuum fields and two external fields with large detunings. Due to the dark resonance, the atoms are trapped in a dark state and one has the maximal coherence between the two ground states. Two double off-resonance stimulated Raman scattering interactions are induced between fields and dressed atoms to establish a dissipative quantum dynamical process based on a collective cavity reservoir. As a result, strong stable spin squeezing is generated, which is verified by our numerical and analytical results. Published by the American Physical Society 2024
For dark resonance, one of the most remarkable coherent effects in light-matter interactions, it has commonly been expected that squeezing and entanglement, if existent, are formed via coherent evolutions against dissipation. Contrary to the expectations, here we show that dissipation generates entanglement between two cavity fields and between two dark-state-based spins. The latter correspond also to the atomic ground-state spin squeezing in a limited parameter domain. The dissipation effects, which are hidden deeply behind the coherence-induced nonlinearities, are extracted by probing into the dressed atom-photon interactions, and are widely applicable for the coherently prepared systems in dark resonances or beyond.
Abstract We present a spin two-axis-twisting mechanism via coherent population trapping (CPT) based atom–photon interactions. CPT happens and the atoms are trapped in the dark state (coherent superposition of two ground states) when the ground states are resonantly coupled to a common excited state. Close to CPT, the atoms behave as two dark-state based spins, which interact with the common cavity vacuum fields. The otherwise nonexistent interaction is created between them and is identified to be responsible for the two-axis-twisting of the ground state spin. The essential difference from the previous schemes is the compatibility of the twisting spin squeezing with the resonant atom-light interaction. The CPT resonant unit serves as a kind of new ingredients for the quantum networks.
We study the effects of equal and unequal Rabi frequencies as well as cavity bandwidth on the optimal noise of the output fields from a two-mode optical cavity, which is fed by two coherent fields and encloses a collection of three-level Λ atoms. Each of the output modes is shown to be highly squeezed in the case of smaller symmetrical atomic detunings compared to the spontaneous-emission rates, where the system is in the vicinity of perfect coherent population trapping (CPT). We find that the squeezing on each output mode is larger than that reported by Dantan et al (2006 Phys. Rev. Lett. 97 023605) when adjusting the equal Rabi frequencies. The cavity bandwidth affects, not the degree of squeezing, but the linewidth of the spectral components. In an alternative way, the squeezing of each outgoing mode can be understood as a consequence of the enhanced cross-phase modulation, different from the nonlinear Faraday effect in Dantan's paper (2006 Phys. Rev. Lett. 97 023605). The application of squeezed light is to obtain high-precision measurement, optical communication, and interferometric detection of gravitational radiation.
Spin twisting is generally not incompatible with steady-state atomic coherence because spin twisting as a representative kind of parametric processes is based on far-off-resonant atom-field interactions while the steady-state atomic coherence is achieved mainly by resonant interactions. Here we propose a resonant plus far-off-resonant scheme to generate the compatibility. The resonant part uses coherent population trapping (CPT) for steady-state maximal atomic coherence, while the far-off-resonant part utilizes Stark shift for a nonlinear response in analog with the motion of a cavity mirror under radiation pressure. The compatible combination CPT with the spin optodymanics analog to cavity optomechanics leads to the spin one- or two-axis-twisting together with steady-state maximal atomic coherence. The general conditions and the parameter regimes for the compatibility are analyzed. This scheme illustrates that the combination of CPT with Stark shift provides an efficient way for the compatibility of the spin twisting squeezing with steady-state maximal atomic coherence.
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.