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 A

Forward-backward analysis of the photon-number evolution in a cavity

T. Rybarczyk, Bruno Peaudecerf, Mariane Penasa, Stefan Gerlich, Brian Julsgaard, Klaus Mølmer, S. Gleyzes, M. Brune, J. M. Raimond, S. Haroche, I. Dotsenko

Published Jun 15, 2015• 53 citations
Publisher

Abstract

A quantum system can be monitored through repeated interactions with meter systems. The state of the system at time $t$, represented by the density matrix $\ensuremath{\rho}(t)$, then becomes conditioned on the information obtained by the meters until that time. More insight in the state of the system at any time $t$ is provided, however, by taking into account the full detection of all meters interacting with the system both in the past and in the future of $t$. We present experiments that use near-resonant atomic probes to monitor the evolution of the quantized field in a cavity. The application of the forward-backward smoothing method to this quantum problem, justified by the past quantum state formalism [S. Gammelmark et al., Phys. Rev. Lett. 111, 160401 (2013)], allows us to resolve a posteriori dynamics, which is not reflected by the usual quantum state $\ensuremath{\rho}(t)$.

DOI
10.1103/physreva.91.062116

Related papers

Past quantum state analysis of the photon number evolution in a cavity

T. Rybarczyk, Stefan Gerlich, Bruno Peaudecerf +8 more

A quantum system can be monitored through repeated interactions with meters, followed by their detection. The state of the system at time t is thus conditioned on the information obtained until that time. More insight in the state dynamics is provided, however, by the past quantum state (PQS) [S. Gammelmark et al. Phys. Rev. Lett. 111, 160401 (2013)]. It relies on all aspects of the system evolution which are recorded in the past and in the future of t. Using PQS analysis for the quantum non-demolition photon number counting in a cavity, we can reveal information hidden in the standard approach and resolve a wider range of number states. This experiment demonstrates the strong potential of PQS analysis.

arXiv:1409.0958•Sep 3, 2014•4 citations

CLEO®/Europe-IQEC 2015, One Page Summary Template Quantum state control with atoms and cavities

Mariane Penasa, T. Rybarczyk, Bruno Peaudecerf +6 more

The estimation of the state of a quantum system is a central task in quantum information and quantum-enabled metrology. A quantum system can be monitored indirectly through its successive interaction with meters, whose final detection provides information on the system’s state. In the standard, forward, approach, the system’s density operator, ρ, at time t is deduced from all measurements performed up to time t and from our knowledge of the system’s dynamics, including relaxation. The recently introduced past quantum state (PQS) formalism [1] provides us with a simple method to include in the state estimation also information gathered after t. We present here an experiment applying the PQS analysis to a system with a high-dimensional Hilbert space [2].

European Quantum Electronics Conference (EQEC)•Jun 21, 2015•0 citations

Quantum jump dynamics in cavity QED

Dominique Spehner, Miguel Orszag

We study the stochastic dynamics of the electromagnetic field in a lossless cavity interacting with a beam of two-level atoms, given that the atomic states are measured after they have crossed the cavity. The atoms first interact at the exit of the cavity with a classical laser field ℰ and then enter into a detector which measures their states. Each measurement disentangles the field and the atoms and changes in a random way the state |ψ(t)〉 of the cavity field. For weak atom-field coupling, the evolution of |ψ(t)〉 when many atoms cross the cavity and the detector is characterized by a succession of quantum jumps occurring at random times, separated by quasi-Hamiltonian evolutions, both of which depend on the laser field ℰ. For ℰ=0, the dynamics is the same as in the Monte Carlo wave function model of Dalibard et al. [Phys. Rev. Lett. 68, 580 (1992)] and Carmichael, An Open System Approach to Quantum Optics, Lecture Notes in Physics Vol. 18 (Springer, Berlin, 1991)]. The density matrix of the quantum field, obtained by averaging the projector |ψ(t)〉〈ψ(t)| over all results of the measurements, is independent of ℰ and follows the master equation of the damped harmonic oscillator at finite temperature. We provide numerical evidence showing that for large ℰ, an arbitrary initial field state |ψ(0)〉 evolves under the monitoring of the atoms and the measurements toward squeezed states |α,re2iφ〉, moving in the α-complex plane but with almost constant squeezing parameters r and φ. The values of r and φ are determined analytically. On the other hand, for ℰ=0, the dynamics transforms the initial state into Fock states |n〉 with fluctuating numbers of photons n, as shown in Kist et al. [J. Opt. B: Quantum Semiclassical Opt. 1, 251 (1999)]. In the last part, we derive the quantum jump dynamics from the linear quantum jump model proposed in Spehner and Bellissard [J. Stat. Phys. 104, 525 (2001)], for arbitrary open quantum systems having a Lindblad-type evolution. A careful derivation of the infinite jump rates limit, where the dynamics can be approximated by a diffusion process of the quantum state, is also presented.

Journal of Mathematical Physics•Jul 1, 2002•8 citations

Manipulation of photons in a cavity by dispersive atom-field coupling: Quantum-nondemolition measurements and generation of ‘‘Schrödinger cat’’ states

M. Brune, S. Haroche, J. M. Raimond +2 more

A quantum-nondemolition method to measure the number of photons stored in a high-Q cavity, introduced by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)], is described in detail. It is based on the detection of the dispersive phase shift produced by the field on the wave function of nonresonant atoms crossing the cavity. This shift can be measured by atomic interferometry, using the Ramsey separated-oscillatory-field method. The information acquired by detecting a sequence of atoms modifies the field step by step, until it eventually collapses into a Fock state. At the same time, the field phase undergoes a diffusive process as a result of the back action of the measurement on the photon-number conjugate variable. Once a Fock state has been generated, its evolution under weak perturbation can be continuously monitored, revealing quantum jumps between various photon numbers. When applied to an initial coherent field, the intermediate steps of the measuring sequence produce quantum superpositions of classical fields, known as ``Schr\"odinger cat states.'' Ways to prepare and detect these states in a cavity subjected to a weak relaxation process are discussed. The effects analyzed in this article could realistically be observed by using circular Rydberg atoms and very high-Q superconducting microwave cavities. The possibility of photon ``manipulation'' through nonresonant atom-field interactions opens a domain in cavity QED studies.

Physical Review A•Apr 1, 1992•737 citations

Colloquium: Manipulating quantum entanglement with atoms and photons in a cavity

J. M. Raimond, M. Brune, S. Haroche

After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.

•Jan 1, 2001•90 citations

Conditional evolution in cavity QED

G. T. Foster, D. Greenbaum, Luis A. Orozco

Summary form only given. The second order intensity correlation function can provide evidence of the non-classical nature of an electric field, as well as information about the dynamics which produce the field. In practice, this is a conditional measurement of the probability to detect a photon given that another photon was detected in coincidence or some time before. We have measured the correlation function of the photons escaping from a strongly coupled cavity QED system consisting of a high finesse interferometer traversed by a beam of optically pumped Rb atoms. In this regime, the rate of reversible exchange of energy between the atoms and the cavity is larger than the cavity decay and spontaneous emission rates, and the saturation photon number is less than one. The correlations exhibit the non-classical features of antibunching and sub-Poissonian statistics, and an oscillation related to the exchange of energy taking place in the coupled system of atoms and cavity field. We view the initial photon detection as causing a projection of the system into a well defined initial state from which it coherently evolves back to steady state. A full characterization of this conditional evolution requires the measurement of the electric field as it evolves from the initial state.

Quantum Electronics and Laser Science Conference•Jan 20, 2003•0 citations
A quantum system can be monitored through repeated interactions with meter systems. The state of the system at time ttt, represented by the density matrix \ensuremathρ(t)\ensuremath{\rho}(t)\ensuremathρ(t), then becomes conditioned on the information obtained by the meters until that time. More insight in the state of the system at any time ttt is provided, however, by taking into account the full detection of all meters interacting with the system both in the past and in the future of ttt. We present experiments that use near-resonant atomic probes to monitor the evolution of the quantized field in a cavity. The application of the forward-backward smoothing method to this quantum problem, justified by the past quantum state formalism [S. Gammelmark et al., Phys. Rev. Lett. 111, 160401 (2013)], allows us to resolve a posteriori dynamics, which is not reflected by the usual quantum state \ensuremathρ(t)\ensuremath{\rho}(t)\ensuremathρ(t).
A quantum system can be monitored through repeated interactions with meters, followed by their detection. The state of the system at time t is thus conditioned on the information obtained until that time. More insight in the state dynamics is provided, however, by the past quantum state (PQS) [S. Gammelmark et al. Phys. Rev. Lett. 111, 160401 (2013)]. It relies on all aspects of the system evolution which are recorded in the past and in the future of t. Using PQS analysis for the quantum non-demolition photon number counting in a cavity, we can reveal information hidden in the standard approach and resolve a wider range of number states. This experiment demonstrates the strong potential of PQS analysis.
The estimation of the state of a quantum system is a central task in quantum information and quantum-enabled metrology. A quantum system can be monitored indirectly through its successive interaction with meters, whose final detection provides information on the system’s state. In the standard, forward, approach, the system’s density operator, ρ, at time t is deduced from all measurements performed up to time t and from our knowledge of the system’s dynamics, including relaxation. The recently introduced past quantum state (PQS) formalism [1] provides us with a simple method to include in the state estimation also information gathered after t. We present here an experiment applying the PQS analysis to a system with a high-dimensional Hilbert space [2].
We study the stochastic dynamics of the electromagnetic field in a lossless cavity interacting with a beam of two-level atoms, given that the atomic states are measured after they have crossed the cavity. The atoms first interact at the exit of the cavity with a classical laser field ℰ and then enter into a detector which measures their states. Each measurement disentangles the field and the atoms and changes in a random way the state |ψ(t)〉 of the cavity field. For weak atom-field coupling, the evolution of |ψ(t)〉 when many atoms cross the cavity and the detector is characterized by a succession of quantum jumps occurring at random times, separated by quasi-Hamiltonian evolutions, both of which depend on the laser field ℰ. For ℰ=0, the dynamics is the same as in the Monte Carlo wave function model of Dalibard et al. [Phys. Rev. Lett. 68, 580 (1992)] and Carmichael, An Open System Approach to Quantum Optics, Lecture Notes in Physics Vol. 18 (Springer, Berlin, 1991)]. The density matrix of the quantum field, obtained by averaging the projector |ψ(t)〉〈ψ(t)| over all results of the measurements, is independent of ℰ and follows the master equation of the damped harmonic oscillator at finite temperature. We provide numerical evidence showing that for large ℰ, an arbitrary initial field state |ψ(0)〉 evolves under the monitoring of the atoms and the measurements toward squeezed states |α,re2iφ〉, moving in the α-complex plane but with almost constant squeezing parameters r and φ. The values of r and φ are determined analytically. On the other hand, for ℰ=0, the dynamics transforms the initial state into Fock states |n〉 with fluctuating numbers of photons n, as shown in Kist et al. [J. Opt. B: Quantum Semiclassical Opt. 1, 251 (1999)]. In the last part, we derive the quantum jump dynamics from the linear quantum jump model proposed in Spehner and Bellissard [J. Stat. Phys. 104, 525 (2001)], for arbitrary open quantum systems having a Lindblad-type evolution. A careful derivation of the infinite jump rates limit, where the dynamics can be approximated by a diffusion process of the quantum state, is also presented.
A quantum-nondemolition method to measure the number of photons stored in a high-Q cavity, introduced by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)], is described in detail. It is based on the detection of the dispersive phase shift produced by the field on the wave function of nonresonant atoms crossing the cavity. This shift can be measured by atomic interferometry, using the Ramsey separated-oscillatory-field method. The information acquired by detecting a sequence of atoms modifies the field step by step, until it eventually collapses into a Fock state. At the same time, the field phase undergoes a diffusive process as a result of the back action of the measurement on the photon-number conjugate variable. Once a Fock state has been generated, its evolution under weak perturbation can be continuously monitored, revealing quantum jumps between various photon numbers. When applied to an initial coherent field, the intermediate steps of the measuring sequence produce quantum superpositions of classical fields, known as ``Schr\"odinger cat states.'' Ways to prepare and detect these states in a cavity subjected to a weak relaxation process are discussed. The effects analyzed in this article could realistically be observed by using circular Rydberg atoms and very high-Q superconducting microwave cavities. The possibility of photon ``manipulation'' through nonresonant atom-field interactions opens a domain in cavity QED studies.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
Summary form only given. The second order intensity correlation function can provide evidence of the non-classical nature of an electric field, as well as information about the dynamics which produce the field. In practice, this is a conditional measurement of the probability to detect a photon given that another photon was detected in coincidence or some time before. We have measured the correlation function of the photons escaping from a strongly coupled cavity QED system consisting of a high finesse interferometer traversed by a beam of optically pumped Rb atoms. In this regime, the rate of reversible exchange of energy between the atoms and the cavity is larger than the cavity decay and spontaneous emission rates, and the saturation photon number is less than one. The correlations exhibit the non-classical features of antibunching and sub-Poissonian statistics, and an oscillation related to the exchange of energy taking place in the coupled system of atoms and cavity field. We view the initial photon detection as causing a projection of the system into a well defined initial state from which it coherently evolves back to steady state. A full characterization of this conditional evolution requires the measurement of the electric field as it evolves from the initial state.