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arXiv:quant-ph/0409160 · Physical Review A

General limit to nondestructive optical detection of atoms

J. J. Hope, J. D. Close

Published Apr 26, 2005• 23 citations
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Abstract

We demonstrate that there is a fundamental limit to the sensitivity of phase-based detection of atoms with light for a given maximum level of allowable spontaneous emission. This is a generalization of previous results for two- and three-level atoms. The limit is due to an upper bound on the phase shift that can be imparted on a laser beam for a given excited-state population. Specifically, we show that no single-pass optical technique using classical light, based on any number of lasers or coherences between any number of levels, can exceed the limit imposed by the two-level atom. This puts significant restrictions on potential nondestructive optical measurement schemes.

DOI
10.1103/physreva.71.043822

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We demonstrate that there is a fundamental limit to the sensitivity of phase-based detection of atoms with light for a given maximum level of allowable spontaneous emission. This is a generalization of previous results for two- and three-level atoms. The limit is due to an upper bound on the phase shift that can be imparted on a laser beam for a given excited-state population. Specifically, we show that no single-pass optical technique using classical light, based on any number of lasers or coherences between any number of levels, can exceed the limit imposed by the two-level atom. This puts significant restrictions on potential nondestructive optical measurement schemes.
All optical techniques used to probe the properties of Bose-Einstein condensates have been based on dispersion and absorption that can be described by a two-level atom. Both phenomena lead to spontaneous emission that is destructive at the low energies involved with ultracold atomic systems. Recently, both were shown to lead to the same limit to the signal to noise ratio for a given destruction. We develop a new method for calculating the phase shift of a laser beam and show that no single-pass optical technique using classical light and a three-level atom can exceed this limit. This puts significant restrictions on potential nondestructive measurement schemes.
We consider atoms traversing a cavity filled with an optical field. When the atoms are well detuned from the optical resonance the output momentum distribution of the atoms is found to be a sensitive probe of the photon statistics of the light field. Near resonance spontaneous emission smears the diffractive peaks. We obtain a good fit to the experimental data of Gould et at. (1991). As the atoms pass through the optical field they impart a position-dependent phase shift to the field. By making a quadrature phase measurement on the optical field a position measurement of the atom is achieved. We show that it is possible to prepare the atom in a 'contractive state' which beats the standard quantum limit for position measurements.
A method for nondestructive characterization of a dipole-trapped atomic sample is presented. It relies on a measurement of the phase shift imposed by cold atoms on an optical pulse that propagates through a free-space Mach-Zehnder interferometer. Using this technique we are able to determine, with very good accuracy, relevant trap parameters such as the atomic sample temperature, trap oscillation frequencies, and loss rates. Another important feature is that our method is faster than conventional absorption or fluorescence techniques, allowing the combination of high-dynamical range measurements and a reduced number of spontaneous emission events per atom.
In atomic and molecular phase measurements using laser-induced fluorescence detection, optical cycling can enhance the effective photon detection efficiency and hence improve sensitivity. We show that detecting many photons per atom or molecule, while necessary, is not a sufficient condition to approach the quantum projection limit for detection of the phase in a two-level system. In particular, detecting the maximum number of photons from an imperfectly closed optical cycle reduces the signal-to-noise ratio (SNR) by a factor of 2\sqrt{2}2​, compared to the ideal case in which leakage from the optical cycle is sufficiently small. We derive a general result for the SNR in a system in terms of the photon detection efficiency, probability for leakage out of the optical cycle per scattered photon, and the product of the average photon scattering rate and total scattering time per atom or molecule.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band-gap structure with one resonant frequency near the edge of the photonic band gap. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This nonzero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field-atom interaction exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive, optical memory device on the atomic scale. The protected electric dipole within the photonic band gap provides a basis for a qubit to encode information for quantum computations.