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arXiv:quant-ph/0604192 · Physical Review A

Atomic entanglement generation with reduced decoherence via four-wave mixing

Claudiu Genes, P. R. Berman

Published Jun 29, 2006• 7 citations
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Abstract

In most proposals for the generation of entanglement in large ensembles of atoms via projective measurements, the interaction with the vacuum is responsible for both the generation of the signal that is detected and the spin depolarization or decoherence. In consequence, one must usually work in a regime where the information acquisition via detection is sufficiently slow (weak measurement regime) such as not to strongly disturb the system. We propose here a four-wave mixing scheme where, owing to the pumping of the atomic system into a dark state, the polarization of the ensemble is not critically affected by spontaneous emission. In the language of spin squeezing, the removal of the limitations imposed by spontaneous emission allows one to work in a strong signal regime where the Heisenberg limit can be reached.

DOI
10.1103/physreva.73.063828

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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.

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In most proposals for the generation of entanglement in large ensembles of atoms via projective measurements, the interaction with the vacuum is responsible for both the generation of the signal that is detected and the spin depolarization or decoherence. In consequence, one must usually work in a regime where the information acquisition via detection is sufficiently slow (weak measurement regime) such as not to strongly disturb the system. We propose here a four-wave mixing scheme where, owing to the pumping of the atomic system into a dark state, the polarization of the ensemble is not critically affected by spontaneous emission. In the language of spin squeezing, the removal of the limitations imposed by spontaneous emission allows one to work in a strong signal regime where the Heisenberg limit can be reached.
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.
We theoretically investigate the entangled states of an atomic ensemble that can be obtained via cavity feedback, varying the atom-light coupling from weak to strong, and including a systematic treatment of decoherence. In the strong-coupling regime for small atomic ensembles, the system is driven by cavity losses into a long-lived, highly entangled many-body state that we characterize analytically. In the weak-coupling regime for large ensembles, we find analytically the maximum spin-squeezing that can be achieved by optimizing both the coupling and the atom number. This squeezing is fundamentally limited by spontaneous emission to a constant value, which is independent of the atom number.
We theoretically investigate the entangled states of an atomic ensemble that can be obtained via cavity feedback, varying the atom-light coupling from weak to strong, and including a systematic treatment of decoherence. In the strong-coupling regime for small atomic ensembles, the system is driven by cavity losses into a long-lived, highly entangled many-body state that we characterize analytically. In the weak-coupling regime for large ensembles, we find analytically the maximum spin-squeezing that can be achieved by optimizing both the coupling and the atom number. This squeezing is fundamentally limited by spontaneous emission to a constant value, which is independent of the atom number.
Squeezed light generated by four-wave mixing near the Na atomic resonance is compared with a full quantum-theoretical model. Losses and dephasing that are due to spontaneous emission near the atomic resonance are included in this theoretical treatment. The experimental results show noise reduction greater than 1 dB below the standard quantum limits and are in good agreement with the quantum model at low pump intensities and large detuning. Theory and experiment show that limits to squeezed-light noise reduction resulting from spontaneous-emission losses can be largely avoided by using nondegenerate four-wave mixing and pump intensities near the atomic saturation values.
The goal of the project is to produce a pair of polarization-entangled light fields using four-wave mixing in hot Rb vapor. In this process, interaction of atoms with near-resonant strong control optical field results in strong amplification of a nearly-collinear probe optical field and in generation of a quantum correlated conjugate Stokes optical field. In order to establish the quantum correlation between the Stokes and probe fields, we have adopted a homodyne detection scheme. If the differential noise between the Stokes and probe fields is below the quantum noise limit, then intensity fluctuation entanglement has been achieved, and it is possible to produce the polarization Bell states.
In general, the process of spin squeezing is employed for atomic sensors that are essentially free from the effect of spontaneous emission. In the case of an atomic clock based on coherent population trapping, spontaneous emission plays a key role. Specifically, when the clock is realized in the Ramsey configuration employing a pair of pulses separated in time, it is the spontaneous emission process during the first pulse that creates the coherent population trapping, by optically pumping the atoms into the so-called dark state. We show in this talk that it is still possible to apply the process of spin squeezing to enhance the sensitivity of such a clock, by designing carefully the sequence of steps in the protocol. Specifically, we consider the approach of using the maximally entangled Schroedinger Cat states, produced via one axis twist squeezing, to achieve Heisenberg Limited sensitivity, representing an improvement in sensitivity by as much as four orders of magnitude.