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

Physical Review Letters

Measurement of Atomic Motion in a Standing Light Field by Homodyne Detection

Ralf Quadt, Matthew J. Collett, Daniel F. Walls

Published Jan 16, 1995• 142 citations
Publisher

Abstract

It is shown that the photocurrent measured using homodyne detection of the phase quadrature on the output field of a cavity gives information about the transverse motion of an atom passing through the standing light field inside the cavity. Monte Carlo simulation techniques are used which result in quantum trajectories of the system conditioned on the measured photocurrent, i.e., the photocurrent defines the backaction of the continuous measurement on the atomic motion.

DOI
10.1103/physrevlett.74.351

Related papers

Localization of an atom by homodyne measurement

A. M. Herkommer, H. J. Carmichael, Wolfgang P. Schleich

We study a continuous homodyne measurement of the field transmitted from an optical cavity. In particular, we investigate the back-action of this measurement onto an atom whose centre-of-mass motion is entangled with the cavity field. Using the method of quantum trajectories we calculate analytically and numerically the time evolution of the entangled quantum state, and demonstrate the localization of the atom relative to the nodes of the cavity field. We compare the quantum trajectory formalism of the continuous homodyne measurement to a projection onto quadrature eigenstates of the field and show that in the long-time limit both descriptions are identical.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Feb 1, 1996•47 citations

Dynamics of the conditional electromagnetic field in cavity QED

Wade P. Smith, Joseph E. Reiner, Luis A. Orozco

Summary form only given. We have developed a correlation technique that permits us to follow the evolution of the mean amplitude of the conditional electromagnetic field emitted from an optical system. The detection of a photon is correlated with the photocurrent record from a balanced homodyne detector. The measured signal in the homodyne detector is proportional to a correlation between particle wave aspects of light. One application of this technique is the measurement of quadrature amplitude fluctuations which violate classical bounds by orders of magnitude.We use this wave-particle correlator to study the time evolution of the electromagnetic field emitted from a cavity QED system. We operate in the optical regime of cavity QED where a beam of optically pumped two-level Rb atoms traverse the TEM/sub 00/ mode of a high finesse Fabry-Perot cavity.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•0 citations

Quantum trajectory calculations in cavity QED

L. Tian, H. J. Carmichael

We use the quantum trajectory (stochastic wave function) approach to simulate the dynamics of a cavity QED system. The system consists of one atom interacting on resonance with one mode of a coherently driven optical cavity. We simulate a variety of different measurements on this system. The simulation of direct photoelectric detection produces trajectories that illustrate the collapse of the wave function in delayed photon coincidence measurements. It also allows us to calculate waiting-time distributions, pho­toelectron counting distributions, and the mean transmitted intensity as a function of the excitation frequency and field strength. A simulation with frequency filtering of the stochastic wave fuction gives results for optical spectra. From a simulation of homodyne detection we obtain trajectories showing the fluctuations in the quadrature phase amplitudes of the intracavity field and the atomic dipole. These simulations are used to calculate spectra of squeezing. We show that when the cavity is excited near one of the "vacuum" Rabi resonances, the composite atom-cavity system behaves like a two-state system. Under these conditions the optical spectrum shows Mollow sidebands caused by a dynamic Stark shift of the Jaynes-Cummings eigenstates. Thus, in this measurement we are observing the "dressing" of the (one-quantum) dressed states.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

Homodyne-like detection scheme based on photon-number-resolving detectors

Alessia Allevi, Matteo Bina, Stefano Olivares +1 more

Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.

International Journal of Quantum Information•Dec 1, 2017•13 citations

Simultaneous continuous measurement of photon-counting and homodyne detection on a free photon field: dynamics of state reduction and the mutual influence of measurement backaction

Yui Kuramochi, Yu Watanabe, Masahito Ueda

We analyze a simultaneous continuous measurement of photon-counting and homodyne detection. The stochastic master equation or stochastic Schrödinger equation describing the measurement process includes both jump-type and diffusive-type stochastic increments. Analytic expressions of the wave function conditioned on homodyne and photon-counting records are obtained, yielding the probability density distributions and generating functions of the measurement records. Formula for the expectation values of the homodyne records conditioned on a photon-counting event is also derived which quantitatively describes the measurement backaction of photon-counting on the homodyne output. The obtained results are applied to typical initial states --- coherent, number, thermal, and squeezed states. Monte Carlo simulations of the measurement processes are also presented to demonstrate the dynamics of the combined measurement process.

arXiv:1212.0968•Journal of Physics A Mathematical and Theoretical•Oct 7, 2013•5 citations

Retroactive Quantum Jumps in a Strongly Coupled Atom-Field System

Hideo Mabuchi, Howard M. Wiseman

We investigate a novel type of conditional dynamic that occurs in the strongly driven Jaynes-Cummings system with dissipation. Extending the work of Alsing and Carmichael [Quantum Opt. 3, 13 (1991)], we present a combined numerical and analytic study of the stochastic master equation that describes the system's conditional evolution when the cavity output is continuously observed via homodyne detection, but atomic spontaneous emission is not monitored at all. We find that quantum jumps of the atomic state are induced by its dynamical coupling to the optical field, in order retroactively to justify atypical fluctuations occurring in the homodyne photocurrent.

arXiv:quant-ph/9807018•Physical Review Letters•Nov 23, 1998•32 citations
It is shown that the photocurrent measured using homodyne detection of the phase quadrature on the output field of a cavity gives information about the transverse motion of an atom passing through the standing light field inside the cavity. Monte Carlo simulation techniques are used which result in quantum trajectories of the system conditioned on the measured photocurrent, i.e., the photocurrent defines the backaction of the continuous measurement on the atomic motion.
We study a continuous homodyne measurement of the field transmitted from an optical cavity. In particular, we investigate the back-action of this measurement onto an atom whose centre-of-mass motion is entangled with the cavity field. Using the method of quantum trajectories we calculate analytically and numerically the time evolution of the entangled quantum state, and demonstrate the localization of the atom relative to the nodes of the cavity field. We compare the quantum trajectory formalism of the continuous homodyne measurement to a projection onto quadrature eigenstates of the field and show that in the long-time limit both descriptions are identical.
Summary form only given. We have developed a correlation technique that permits us to follow the evolution of the mean amplitude of the conditional electromagnetic field emitted from an optical system. The detection of a photon is correlated with the photocurrent record from a balanced homodyne detector. The measured signal in the homodyne detector is proportional to a correlation between particle wave aspects of light. One application of this technique is the measurement of quadrature amplitude fluctuations which violate classical bounds by orders of magnitude.We use this wave-particle correlator to study the time evolution of the electromagnetic field emitted from a cavity QED system. We operate in the optical regime of cavity QED where a beam of optically pumped two-level Rb atoms traverse the TEM/sub 00/ mode of a high finesse Fabry-Perot cavity.
We use the quantum trajectory (stochastic wave function) approach to simulate the dynamics of a cavity QED system. The system consists of one atom interacting on resonance with one mode of a coherently driven optical cavity. We simulate a variety of different measurements on this system. The simulation of direct photoelectric detection produces trajectories that illustrate the collapse of the wave function in delayed photon coincidence measurements. It also allows us to calculate waiting-time distributions, pho­toelectron counting distributions, and the mean transmitted intensity as a function of the excitation frequency and field strength. A simulation with frequency filtering of the stochastic wave fuction gives results for optical spectra. From a simulation of homodyne detection we obtain trajectories showing the fluctuations in the quadrature phase amplitudes of the intracavity field and the atomic dipole. These simulations are used to calculate spectra of squeezing. We show that when the cavity is excited near one of the "vacuum" Rabi resonances, the composite atom-cavity system behaves like a two-state system. Under these conditions the optical spectrum shows Mollow sidebands caused by a dynamic Stark shift of the Jaynes-Cummings eigenstates. Thus, in this measurement we are observing the "dressing" of the (one-quantum) dressed states.
Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.
We analyze a simultaneous continuous measurement of photon-counting and homodyne detection. The stochastic master equation or stochastic Schrödinger equation describing the measurement process includes both jump-type and diffusive-type stochastic increments. Analytic expressions of the wave function conditioned on homodyne and photon-counting records are obtained, yielding the probability density distributions and generating functions of the measurement records. Formula for the expectation values of the homodyne records conditioned on a photon-counting event is also derived which quantitatively describes the measurement backaction of photon-counting on the homodyne output. The obtained results are applied to typical initial states --- coherent, number, thermal, and squeezed states. Monte Carlo simulations of the measurement processes are also presented to demonstrate the dynamics of the combined measurement process.
We investigate a novel type of conditional dynamic that occurs in the strongly driven Jaynes-Cummings system with dissipation. Extending the work of Alsing and Carmichael [Quantum Opt. 3, 13 (1991)], we present a combined numerical and analytic study of the stochastic master equation that describes the system's conditional evolution when the cavity output is continuously observed via homodyne detection, but atomic spontaneous emission is not monitored at all. We find that quantum jumps of the atomic state are induced by its dynamical coupling to the optical field, in order retroactively to justify atypical fluctuations occurring in the homodyne photocurrent.