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Physical Review A

Quantum nondemolition measurement of small photon numbers using stored light

L. Liang, Guang Lin, Yaming Hao, Yueping Niu, Shuang Gong

Published Nov 3, 2014• 8 citations
Publisher

Abstract

We propose a scheme for realizing a quantum nondemolition (QND) measurement of a small number of optical photons. Our scheme has two stages: First, we couple a propagating light pulse with fixed photon number to a trapped cold atomic gas within a cavity, such that the pulse is stored within a collective polariton mode. Second, a small-photon-number measurement is engineered by monitoring the cavity-transmission spectrum. Since the polariton mode profile is preserved during the process of detecting the spectrum, photon-number QND measurements could be achieved by retrieving the light pulse from the polariton mode. We also discuss a method which uses QND measurements to generate small-photon Fock states.

DOI
10.1103/physreva.90.055801

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We propose a scheme for realizing a quantum nondemolition (QND) measurement of a small number of optical photons. Our scheme has two stages: First, we couple a propagating light pulse with fixed photon number to a trapped cold atomic gas within a cavity, such that the pulse is stored within a collective polariton mode. Second, a small-photon-number measurement is engineered by monitoring the cavity-transmission spectrum. Since the polariton mode profile is preserved during the process of detecting the spectrum, photon-number QND measurements could be achieved by retrieving the light pulse from the polariton mode. We also discuss a method which uses QND measurements to generate small-photon Fock states.
We propose a technique for quantum nondemolition (QND) measurement and heralded preparation of Fock states by dynamics of electromagnetically induced transparency (EIT). An atomic ensemble trapped in an optical cavity is driven by two external continuous-wave classical fields to form EIT in steady state. As soon as a weak coherent field is injected into the cavity, the EIT system departs from steady state, falls into transient state dynamics by the dispersive coupling between cavity injected photons and atoms. Because the imaginary part of time-dependent linear susceptibility Im[X(t)] of the atomic medium explicitly depends on the number n of photons during the process of transient state dynamics, the measurement on the change of transmission of the probe field can be used for QND measurement of small photon number, and thus create the photon Fock states in particular single-photon state in a heralded way.
We propose a quantum nondemolition measurement of the photon-number distribution for a two-mode cavity field. In the scheme two sequences of two-level atoms interact dispersively with the respective cavity modes and resonantly with two classical fields, and then are detected continually. The field finally reduces to a two-mode Fock state. The probability of collapsing to a given Fock state is determined by the initial photon-number distribution. The scheme can be easily generalized to a field with N modes.
We analyze schemes for performing quantum nondemolition (QND) measurements in optical cavities. We consider three schemes: (1) measurement of a quadrature phase amplitude using a parametric process, (2) measurement of a quadrature phase amplitude using the optical Kerr effect in a nonlinear fiber, and (3) measurement of the photon number also using the Kerr effect in a fiber. We show that in the second scheme an enhancement of the QND effect may be obtained by making the cavity finesse for the signal larger than that for the probe.
We analyze in detail the quantum-nondemolition (QND) scheme of Brune et al. [Phys. Rev. Lett. 65, 976 (1990)]. It is shown that the quantum treatment of the scheme based on the density-matrix formalism is fully equivalent to an information-theoretical description. In this context, it is explicitly seen that the scheme works well even with a low detection efficiency. We show further that a careful choice of the atomic velocities can significantly reduce the number of atoms needed to perform a measurement. It is also possible to use a monoenergetic atomic beam, although in this case the number of atoms needed increases. Finally we discuss how the results are modified if the atomic velocities are only known approximately.