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A Scheme for Measuring the Relative phase of Two Independent Coherent Probe Fields

Xiong-Jun Liu, Mo‐Lin Ge, X J Zhou

Published Jan 5, 2004• 0 citations
OpenAlex

Abstract

The transfer technique of quantum states from a pair of pump fields to collective atomic excitation in a double $\\Lambda$ type system is extended to matter waves in this paper. For this a scheme for measuring the relative phase of two independent coherent probe fields is proposed in this paper.

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The transfer technique of quantum states from a pair of pump fields to collective atomic excitation in a double Lambda\\LambdaLambda type system is extended to matter waves in this paper. For this a scheme for measuring the relative phase of two independent coherent probe fields is proposed in this paper.
We theoretically examine the quantum-state transfer process from light to a continuous atom laser by extending the original Fleischhauer-Gong scheme [M. Fleischhauer and S. Gong, 88, 070404 (2002)] to a double-$\ensuremath{\Lambda}$ atomic system. We find that the intensity of the output matter waves is controlled by the relative phase of two coherent probe lights, which may provide an interesting method for the measurement of the initial relative phase of two independent light sources.
A scheme is discussed that allows for performing homodyne detection of the matter-wave field of ultracold bosonic atoms. It is based on a pump-probe laser setup, which both illuminates a Bose-Einstein condensate, acting as reference system, and a second ultracold gas, composed by the same atoms but in a quantum phase to determine. Photon scattering outcouples atoms from both systems, which then propagate freely. Under appropriate conditions, when the same photon can either be scattered by the Bose-Einstein condensate or by the other quantum gas, both flux of outcoupled atoms and scattered photons exhibit oscillations, the amplitude of which is proportional to the condensate fraction of the quantum gas. The setup can be extended to measure the first-order correlation function of a quantum gas. The dynamics discussed here makes use of the entanglement between atoms and photons, which is established by the scattering process in order to access detailed information on the quantum state of matter.
We propose a light-scattering scheme to measure the relative phase of atomic Bose-Einstein condensates and its diffusion rate. The proposal relies on the existence of two independent condensates coupled to a common excited state. To this end, we consider a two-well ground-state potential together with excited-state trap wave functions that extend over the whole region. When the first trap is driven by a weak monochromatic laser field, the light scattered from the second trap has a nonzero mean-electric field amplitude with a phase shift proportional to the difference of the condensate phases. When both condensates are driven, the phases of the two laser fields can be adjusted to cancel the scattering completely by a quantum interference. The particular value of the laser phase difference that gives zero scattering determines the relative phase of the two condensates.
A scheme is proposed, that allows one for performing homodyne detection of the matter-wave field of ultracold bosonic atoms. It is based on a pump-probe lasers setup, that both illuminates a Bose-Einstein condensate, acting as reference system, and a second ultracold gas, composed by the same atoms but in a quantum phase to determine. Photon scattering outcouples atoms from both systems, which then propagate freely. Under appropriate conditions, when the same photon can either be scattered by the Bose-Einstein condensate or by the other quantum gas, both flux of outcoupled atoms and scattered photons exhibit oscillations, whose amplitude is proportional to the condensate fraction of the quantum gas. This setup allows one, for instance, to perform thermometry of a condensate or to monitor the Mott-insulator/superfluid phase transition in optical lattices, and can be extended in order to measure the first-order correlation function of a quantum gas. The dynamics here discussed make use of the entanglement between atoms and photons, which is established by the scattering process, in order to access detailed information on the quantum state of matter.
Two-component entangled atom laser is obtained via quantum state transfer technique from lights to matter waves in a five-level MMM-type system. The considered atom-atom collisions can yield an effective Kerr susceptibility for this system and lead to the self- and cross- phase modulation between the two output atom lasers. This effect results in generation of entangled states of output atom lasers. Particularly, a potential application for a quantum phase gate between two individual atom lasers can be demonstrated for the case that the input quantized probe lights are both in the single-photon state.
An experiment is described which is an analog of Young's double-slit interferometer using an atomic electron instead of light. Two phase-coherent laser pulses are used to excite a single electron into a state of the form of a pair of Rydberg wave packets that are initially on opposite sides of the orbit. The two wave packets propagate and spread until they completely overlap, then a third phase-coherent laser pulse probes the resulting fringe pattern. The relative phase of the two wave packets is varied so that the interference produces a single localized electron wave packet on one side of the orbit or the other.