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Journal of Modern Optics

Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering

M. G. Raymer

Published Jun 18, 2004• 40 citations
Publisher

Abstract

A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.

DOI
10.1080/09500340408232488

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Acta Physica Sinica•Dec 30, 2020•1 citation
A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.
We analyze quantum entanglement of Stokes light and atomic electronic polarization excited during single-pass, linear-regime, stimulated Raman scattering in terms of optical wave-packet modes, and atomic-ensemble spatial modes. The output of this process is confirmed to be decomposable into multiple discrete, Bosonic mode pairs, each pair undergoing independent evolution into a two-mode squeezed state. For this we extend the Bloch-Messiah reduction theorem, previously known for discrete linear systems [S. L. Braunstein, Phys. Rev. A 71, 055801 (2005)]. We present typical mode functions in the case of one-dimensional scattering in an atomic vapor. We find that in the absence of dispersion, one mode pair dominates the process, leading to a simple interpretation of entanglement in this continuous-variable system. However, many mode pairs are excited in the presence of dispersion-induced temporal walkoff of the Stokes, as witnessed by the photon-count statistics. We also consider the readout of the stored atomic polarization using the anti-Stokes scattering process. We prove that the readout process can also be decomposed into multiple mode pairs, each pair undergoing independent evolution analogous to a beam-splitter transformation. We show that this process can have unit efficiency under realistic experimental conditions. The shape of the output light wave packet can be predicted. In the case of unit readout efficiency it contains only excitations originating from a specified atomic excitation mode.
In this paper we consider the optical coupling of two four-level atoms via cooperative Raman scattering of correlated photons of the nondegenerate spontaneous parametric radiation. The Raman scattering of twin photons incident on the atoms is additionally stimulated by coherent classical radiation in such a way that it is slightly off resonant for each atom considered independently but resonant for the joint system. We discuss the special excitation conditions when the amplitude of the cooperative stimulated Raman scattering from quantum to classical modes becomes greater than the normal transition rates associated with independent Raman scattering. In certain conditions weak entanglement between the Zeeman sublevels in the ground states of these atoms can appear. The small admixture of entanglement in the system of two atoms leads to strong entanglement between transverse macroscopic spin fluctuations of two spatially separated atomic ensembles coupled by such quantum light. The proposed mechanism of entanglement is relevant to the ground state spin subsystem of two distant macroscopic and optically thin atomic ensembles. Such an entangled state can be stored for a long time and used as a basic Einstein-Podolsky-Rosen system in different applications pursuing the goal of spreading quantum information schemes in atomic subsystems.
This thesis presents a study of the four-wave mixing process in hot Rubidium vapor and its applicability to generating arbitrary quantum states, both in the optical domain and as atomic collective spin excitations. The four-wave mixing process involves a double Raman scattering event, where conservation of energy and momentum entangle these Raman-scattered photons. Heralding upon detection of one of these photons in a given mode projects the other photon onto a single photon Fock state in a well-defined mode, which may serve as a narrowband quantum light source that is compatible with atom-based quantum communication protocols. We integrate the existing technique of conditional measurements into our detection scheme, which allows us to engineer more complex quantum states. Experimentally we demonstrate the production of arbitrary superpositions of |0> and |1> in the optical Fock basis. We also present a theoretical model of this process which incorporates experimental complications such as losses, higher photon-number states, and a non-trivial temporal mode. This scheme can be extended to generate arbitrary quantum states with increasing photon numbers, at the expense of repetition rate. The atomic nature of this four-wave mixing process has an added benefit in that it allows access to excitations of the collective atomic ensemble. The optical results demonstrate the creation of transient collective spin excitations, and we present a proposal to extend this work to generate longer lived arbitrary collective atomic states.
We propose a scheme of generating and verifying mesoscopic-level entanglement between two atomic ensembles using nonresonant stimulated Raman scattering. Entanglement can be generated by direct detection or balanced homodyne detection of the Stokes fields from the two cells after they interfere on a beam splitter. The entanglement of the collective atomic fields can be transferred to the anti-Stokes fields in a readout process. By measuring the operator moments of the anti-Stokes fields, we can verify the presence of entanglement. We model the effects of practical factors such as Stokes-field detector quantum efficiency and additive thermal noise in the entanglement generating process, and anti-Stokes-field losses in the entanglement verification process, and find achievable regimes in which entanglement can be verified at the levels of tens to hundreds of atomic excitations in the ensembles.
Quantum entanglement is an essential quantum resource. With the development of quantum information science, quantum network consisting of quantum nodes and quantum channels has attracted extensive attention. The development of quantum information network requires the capability of generating, storing and distributing quantum entanglement among multiple quantum nodes. It is significant to construct the quantum information, and it has very important applications in the distributed quantum computation and quantum internet. Here we propose a simple and feasible scheme to deterministically entangle three distant atomic ensembles via the interference and feedforward network of the light-atom mixed entanglement. Firstly, three atomic ensembles placed at three remote nodes in a quantum network are prepared into the mixed entangled state of light and atomic ensembles via the spontaneous Raman scattering (SRS) process. Then, the first and second Stokes optical field are interfered on an R1∶T1 optical beam splitter (BS1), and one of the output optical fields from the first optical beam splitter is interfered with the third Stokes field on the second R2∶T2 optical beam splitter (BS2). The quantum fluctuations of the amplitude and phase quadratures of these three output optical fields from BS1 and BS2 are detected by three sets of balanced homodyne detectors, respectively. Finally, the detected signals of the amplitude and phase quadratures are fed to the three atomic ensembles via the radio frequency coils to establish the entanglement among three remote atomic ensembles. At the user-controlled time, three read optical pulses can be applied to these three atomic ensembles to convert the stored entangled state from the atomic spin waves into the anti-Stokes optical fields via the SRS process. According to the tripartite inseparability criterion, the correlation variance combinations of these three anti-Stokes optical fields can be used to verify the performance of entanglement of three atomic ensembles. This scheme can be extended to larger-scale quantum information network with different physical systems and more atomic nodes. Moreover, the entanglement distillation can be combined with this scheme to realize the entanglement among longer distance quantum nodes.