Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

Atomic quantum non-demolition measurements and squeezing

A. Kuzmich, N. P. Bigelow, L. Mandeļ

Published Jun 1, 1998• 308 citations
Publisher

Abstract

We show that the accuracy of atomic interferometry can be improved by using QND measurements of the atomic populations at the inputs to the interferometer. The accuracy of such a scheme surpasses the standard quantum limit of phase measurement δϕ SQL = 1/√ N and could reach the Heisenberg limit δϕ ∼ 1/ N . We propose to perform QND measurements of atomic populations with an off-resonant laser field. The conditions necessary for this kind of QND measurement could be fulfilled in a variety of ways with current experimental techniques, including magneto-optical traps and atomic cells.

DOI
10.1209/epl/i1998-00277-9

Related papers

Quantum-noise-limited interferometric measurement of atomic noise: Towards spin squeezing on the Cs clock transition

Daniel Oblak, Plamen G. Petrov, Carlos L. Garrido Alzar +5 more

We investigate theoretically and experimentally a nondestructive interferometric measurement of the state population of an ensemble of laser-cooled and trapped atoms. This study is a step toward generation of (pseudo)spin squeezing of cold atoms targeted at the improvement of the cesium clock performance beyond the limit set by the quantum projection noise of atoms. We calculate the phase shift and the quantum noise of a near-resonant optical probe pulse propagating through a cloud of cold $^{133}\mathrm{Cs}$ atoms. We analyze the figure of merit for a quantum nondemolition (QND) measurement of the collective pseudospin and show that it can be expressed simply as a product of the ensemble optical density and the pulse-integrated rate of the spontaneous emission caused by the off-resonant probe light. Based on this, we propose a protocol for the sequence of operations required to generate and utilize spin squeezing for the improved atomic clock performance via a QND measurement on the probe light. In the experimental part we demonstrate that the interferometric measurement of the atomic population can reach a sensitivity of the order of $\sqrt{{N}_{\mathrm{at}}}$ in a cloud of ${N}_{\mathrm{at}}$ cold atoms, which is an important benchmark toward the experimental realization of the theoretically analyzed protocol.

arXiv:quant-ph/0312165•Physical Review A•Apr 11, 2005•77 citations

Differential atom interferometry beyond the standard quantum limit

K. Eckert, P. Hyllus, Dagmar Bruß +6 more

We analyze methods designed to go beyond the standard quantum limit for a class of atomic interferometers, where the quantity of interest is the difference of phase shifts obtained by two independent atomic ensembles. An example is given by an atomic Sagnac interferometer, where for two ensembles propagating in opposite directions in the interferometer this phase difference encodes the angular velocity of the experimental setup. We discuss methods of separately or jointly squeezing observables of the two atomic ensembles, and compare in detail the advantages and drawbacks of such schemes. In particular, we show that the method of joint squeezing may improve the variance by up to a factor of 2. We take into account fluctuations of the number of atoms in both the preparation and the measurement stage, and obtain bounds on the difference between the numbers of atoms in the two ensembles, as well as on the detection efficiency, which have to be fulfilled in order to surpass the standard quantum limit. Under realistic conditions, the performance of both schemes can be improved significantly by reading out the phase difference via a quantum nondemolition measurement. Finally, we discuss a scheme using macroscopically entangled ensembles.

arXiv:quant-ph/0507061•Physical Review A•Jan 18, 2006•34 citations

Quantum non-demolition measurement of photon number with atom-light interferometers

Shuying Chen, Liang Chen, Z. Y. Ou +1 more

When atoms are illuminated by an off-resonant field, the AC Stark effect will lead to phase shifts in atomic states. The phase shifts are proportional to the photon number of the off-resonant illuminating field. By measuring the atomic phase with newly developed atom-light hybrid interferometers, we can achieve quantum non-demolition measurement of the photon number of the optical field. In this paper, we analyze theoretically the performance of this QND measurement scheme by using the QND measurement criteria established by Holland et al [Phys. Rev. A 42, 2995 (1990)]. We find the quality of the QND measurement depends on the phase resolution of the atom-light hybrid interferometers. We apply this QND measurement scheme to a twin-photon state from parametric amplifier to verify the photon correlation in the twin beams. Furthermore, a sequential QND measurement procedure is analyzed for verifying the projection property of quantum measurement and for the quantum information tapping. Finally, we discuss the possibility for single-photon-number-resolving detection via QND measurement.

Optics Express•Dec 7, 2017•13 citations

Trapped single atoms and atomic ensembles : quantum computation, coherent manipulation, and interferometry

K. Eckert

techniques from quantum optics, which are realized here through the tunneling interaction among three trapped states.The final part of this thesis focuses on a different regime of the manipulation of neutral atoms, namely on the use of ensembles containing a large number of atoms for the purpose of atom interferometry.More precisely, differential interferometers are studied, where the quantity of interest is encoded in the difference of two phases obtained by two independent atomic ensembles.Methods using separately or jointly squeezed states of the two atomic ensembles are discussed, which allow to surpass the standard quantum limit to the resolution of the interferometer.It is shown that non-local squeezing gives an optimal method, provided that certain conditions on the preparation and read-out of the atomic ensembles are met.Under realistic conditions the performance of both schemes can be further improved by reading out the phase difference via a quantum non-demolition measurement.

•Jan 1, 2005•0 citations

Improving Kerr QND measurement sensitivity via squeezed light

Stepan N. Balybin, Dariya Salykina, Khalili, Farid Ya.

In ref [Phys. Rev. A 106, 013720], the scheme of quantum non-demolition measurement of optical quanta that uses a resonantly enhanced Kerr nonlinearity in optical microresonators was analyzed theoretically. It was shown that using the modern high-Q microresonators, it is possible to achieve the sensitivity several times better than the standard quantum limit. Here we propose and analyze in detail a significantly improved version of that scheme. We show, that by using a squeezed quantum state of the probe beam and the anti-squeezing (parametric amplification) of this beam at the output of the microresonator, it is possible to reduce the measurement imprecision by about one order of magnitude. The resulting sensitivity allows to generate and verify multi-photon non-Gaussian quantum states of light, making the scheme considered here interesting for the quantum information processing tasks.

arXiv:2210.00857•Oct 3, 2022•0 citations

Optical quantum non-demolition measurements

Philippe Grangier, J.-Ph. Poizat, Jean-François Roch

We discuss some theoretical and experimental aspects of quantum non-demolition (QND) measurements in the optical domain. The efficiency of a QND measurement can be characterized using three criteria, which describe respectively the quality of the quantum measurement, the non-destruction of the signal, and the conditional variance of the output signal beam, given the output meter beam (quantum-state-preparation criterion). Quantitative limits can be defined with respect to these criteria, delimiting "classical" and "quantum" domains of operation. We describe the implementation of two experiments which fulfill these criteria, using either three-level atoms inside a doubly-resonant optical cavity, or semiconductors emitters and receivers.

Physica Scripta•Jan 1, 1994•3 citations
We show that the accuracy of atomic interferometry can be improved by using QND measurements of the atomic populations at the inputs to the interferometer. The accuracy of such a scheme surpasses the standard quantum limit of phase measurement δϕ SQL = 1/√ N and could reach the Heisenberg limit δϕ ∼ 1/ N . We propose to perform QND measurements of atomic populations with an off-resonant laser field. The conditions necessary for this kind of QND measurement could be fulfilled in a variety of ways with current experimental techniques, including magneto-optical traps and atomic cells.
We investigate theoretically and experimentally a nondestructive interferometric measurement of the state population of an ensemble of laser-cooled and trapped atoms. This study is a step toward generation of (pseudo)spin squeezing of cold atoms targeted at the improvement of the cesium clock performance beyond the limit set by the quantum projection noise of atoms. We calculate the phase shift and the quantum noise of a near-resonant optical probe pulse propagating through a cloud of cold 133Cs^{133}\mathrm{Cs}133Cs atoms. We analyze the figure of merit for a quantum nondemolition (QND) measurement of the collective pseudospin and show that it can be expressed simply as a product of the ensemble optical density and the pulse-integrated rate of the spontaneous emission caused by the off-resonant probe light. Based on this, we propose a protocol for the sequence of operations required to generate and utilize spin squeezing for the improved atomic clock performance via a QND measurement on the probe light. In the experimental part we demonstrate that the interferometric measurement of the atomic population can reach a sensitivity of the order of Nat\sqrt{{N}_{\mathrm{at}}}Nat​​ in a cloud of Nat{N}_{\mathrm{at}}Nat​ cold atoms, which is an important benchmark toward the experimental realization of the theoretically analyzed protocol.
We analyze methods designed to go beyond the standard quantum limit for a class of atomic interferometers, where the quantity of interest is the difference of phase shifts obtained by two independent atomic ensembles. An example is given by an atomic Sagnac interferometer, where for two ensembles propagating in opposite directions in the interferometer this phase difference encodes the angular velocity of the experimental setup. We discuss methods of separately or jointly squeezing observables of the two atomic ensembles, and compare in detail the advantages and drawbacks of such schemes. In particular, we show that the method of joint squeezing may improve the variance by up to a factor of 2. We take into account fluctuations of the number of atoms in both the preparation and the measurement stage, and obtain bounds on the difference between the numbers of atoms in the two ensembles, as well as on the detection efficiency, which have to be fulfilled in order to surpass the standard quantum limit. Under realistic conditions, the performance of both schemes can be improved significantly by reading out the phase difference via a quantum nondemolition measurement. Finally, we discuss a scheme using macroscopically entangled ensembles.
When atoms are illuminated by an off-resonant field, the AC Stark effect will lead to phase shifts in atomic states. The phase shifts are proportional to the photon number of the off-resonant illuminating field. By measuring the atomic phase with newly developed atom-light hybrid interferometers, we can achieve quantum non-demolition measurement of the photon number of the optical field. In this paper, we analyze theoretically the performance of this QND measurement scheme by using the QND measurement criteria established by Holland et al [Phys. Rev. A 42, 2995 (1990)]. We find the quality of the QND measurement depends on the phase resolution of the atom-light hybrid interferometers. We apply this QND measurement scheme to a twin-photon state from parametric amplifier to verify the photon correlation in the twin beams. Furthermore, a sequential QND measurement procedure is analyzed for verifying the projection property of quantum measurement and for the quantum information tapping. Finally, we discuss the possibility for single-photon-number-resolving detection via QND measurement.
techniques from quantum optics, which are realized here through the tunneling interaction among three trapped states.The final part of this thesis focuses on a different regime of the manipulation of neutral atoms, namely on the use of ensembles containing a large number of atoms for the purpose of atom interferometry.More precisely, differential interferometers are studied, where the quantity of interest is encoded in the difference of two phases obtained by two independent atomic ensembles.Methods using separately or jointly squeezed states of the two atomic ensembles are discussed, which allow to surpass the standard quantum limit to the resolution of the interferometer.It is shown that non-local squeezing gives an optimal method, provided that certain conditions on the preparation and read-out of the atomic ensembles are met.Under realistic conditions the performance of both schemes can be further improved by reading out the phase difference via a quantum non-demolition measurement.
In ref [Phys. Rev. A 106, 013720], the scheme of quantum non-demolition measurement of optical quanta that uses a resonantly enhanced Kerr nonlinearity in optical microresonators was analyzed theoretically. It was shown that using the modern high-Q microresonators, it is possible to achieve the sensitivity several times better than the standard quantum limit. Here we propose and analyze in detail a significantly improved version of that scheme. We show, that by using a squeezed quantum state of the probe beam and the anti-squeezing (parametric amplification) of this beam at the output of the microresonator, it is possible to reduce the measurement imprecision by about one order of magnitude. The resulting sensitivity allows to generate and verify multi-photon non-Gaussian quantum states of light, making the scheme considered here interesting for the quantum information processing tasks.
We discuss some theoretical and experimental aspects of quantum non-demolition (QND) measurements in the optical domain. The efficiency of a QND measurement can be characterized using three criteria, which describe respectively the quality of the quantum measurement, the non-destruction of the signal, and the conditional variance of the output signal beam, given the output meter beam (quantum-state-preparation criterion). Quantitative limits can be defined with respect to these criteria, delimiting "classical" and "quantum" domains of operation. We describe the implementation of two experiments which fulfill these criteria, using either three-level atoms inside a doubly-resonant optical cavity, or semiconductors emitters and receivers.