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

Journal of Physics B Atomic Molecular and Optical Physics

Probing the quantum state in a cavity via atomic two-photon transitions

Si-de Du, Zhou Lu-wei, Zhizhan Xu, Wenqi Zhang, Yuan Li

Published Nov 14, 1998• 7 citations
Publisher

Abstract

This paper contains a theoretical treatment of a scheme for determining phase-dependent features of a single mode of quantized light fields in general states. The proposal involves using a three-level atom, in a cascade configuration, as a detector. The cascade atom, which is on two-photon resonance with the field, is prepared in a coherent superposition of the upper and lower levels, and detection involves measuring the probability of the cascade atom being in the upper level. The results depend on the phase difference between the amplitudes for the field being in N and N + 2 photon states in the number state basis, and are important in describing nonclassical states, such as squeezed and Schrödinger cat states. The analysis is based on a standard dressed atom model approach and a Fourier treatment of the measured signal. The experimental possibilities of realizing this scheme are also discussed.

DOI
10.1088/0953-4075/31/21/019

Related papers

Generation and detection of nonclassical field states by conditional measurements following two-photon resonant interactions

B. M. Garraway, Boris Sherman, H. M. Moya-Cessa +2 more

A simple scheme is presented that allows the generation and detection of nonclassical states of the electromagnetic (em) field with controllable (predetermined) photon-number and phase distributions. It is based on the two-photon resonant interaction of a single em field mode in a high-Q cavity with initially excited atoms crossing the cavity sequentially (one at a time). The sequence duration should be much shorter than the cavity-mode lifetime. Nonclassical states of the field are generated conditionally, by selecting only those sequences wherein each atom is measured to be in the excited state after the interaction. The field distribution resulting from a sequence of N such measurements is peaked about 2N positions in the phase plane, which evolve sinusoidally as a function of the atomic transit times and are therefore simply controlled. When these peaks are chosen not to overlap, the field state constitutes a generalized Schr\"odinger cat. By choosing them to overlap, we can make parts of the field distribution strongly interfere, giving rise to decimation of the photon-number distribution. In particular, this process can prepare Fock states with controlled photon numbers. The generated phase distribution can be detected by monitoring the pattern of revivals in the excitation of a ``probe'' atom.

Physical Review A•Jan 1, 1994•164 citations

Preparation and detection of macroscopic quantum superpositions by two-photon field-atom interactions

Boris Sherman, Gershon Kurizki

We put forward a simple, feasible scheme for the preparation and subsequent detection of macroscopic quantum superposition (MQS) states. It is based on the two-photon model which obtains when a cascade of two atomic transitions is resonant with twice the field frequency. The initial conditions amount to a field in a mixed state characteristic of lasers or masers and an excited atom. The MQS is generated by a conditional measurement of the atomic excitation after an interaction time that determines the relative phase of the MQS components. Remarkably, the MQS is subsequently detected and its phase is inferred by measuring the excitation probability of a second, ``probe,'' atom, as a function of its interaction time. The realization of the scheme in the optical domain, using dielectric microspheres, is discussed.

Physical Review A•Jun 1, 1992•60 citations

Single-Atom Conditional Manipulation of Confined Quantized Electromagnetic Field

Anna Napoli

It has been recently shown [1] that, under suitable conditions, the interaction between a three-level atom and the quantized field of a bimodal microcavity may be effectively reduced to the two-photon coupling between a single two-level atom and the electromagnetic field in the resonator. The corresponding Hamiltonian model is characterized by intensity-dependent Stark shifts due to the presence of an intermediate off-resonance atomic level. Assume the cavity field prepared at in an arbitrary state and let an initially excited atom cross the cavity with an appropriately selected velocity. It is possible to show that, exploiting a single conditional measurement of the atomic state immediately after the atom leaves the resonator, the bimodal field is projected into a new state characterized by the same photon number distribution present at More in detail, the experimental scheme we propose makes it possible manipulating only the phases of the initial probability amplitudes of finding a well defined population in the cavity. We prove that the state into which the cavity collapses after a successful atomic measurement is unitarily related to the initial field state and the explicit form of the accomplishing operator is constructed. We wish to remark that, beside its inherent theoretical interest, this simple experimental scheme might also be of relevance in the socalled field of quantum communication [2], where implementing unitary modifications of a quantum state signal represents an issue of topical and central importance. More in general, our proposal provides a systematic procedure for controlling selected properties of a quantum state. We in fact demonstrate that our experimental scheme may be reliably exploited to generate orthogonal states to a prefixed one or to control the squeezing direction.

Kluwer Academic Publishers eBooks•Mar 5, 2006•0 citations

Determining the state of a single cavity mode from photon statistics

Kurt A. Jacobs, P. L. Knight, Vlatko Vedral

We present various schemes for measuring the quantum state of a single mode of the electromagnetic field. These involve measuring the photon statistics for the mode before and after an interaction with either one or two two-level atoms. The photon statistics conditioned on the final state of the atoms, for two choices of the initial set of atomic states, along with the initial photon statistics, may be used to calculate the complete quantum state in a simple manner. Alternatively, when one atom is used, two unconditioned sets of photon statistics, each after interaction with a single atom in different initial states, along with the initial photon statistics may be used to calculate the initial state in a simple manner. When the cavity is allowed to interact with just one atom, only pure cavity states which do not contain zeros in the photon distribution may be reconstructed. When two atoms are used we may reconstruct pure states which do not contain adjacent zeros in the photon distribution. Coherent states and number states are among those that may be measured with one-atom interaction, and squeezed states and ‚Schrödinger cats‘ are among those that may be measured with a two-atom interaction.

Journal of Modern Optics•Nov 1, 1997•6 citations

Atomic Bell measurement via two-photon interactions

Carlos A. González-Gutiérrez, Juan Mauricio Torres

We introduce a complete Bell measurement on atomic qubits based on two-photon interactions with optical cavities and discrimination of coherent states of light. The dynamical system is described by the Dicke model for two three-level atoms interacting in two-photon resonance with a single mode of the radiation field, which is known to effectively generate a nonlinear two-photon interaction between the field and two states of each atom. For initial coherent states with a large mean photon number, the field state is well represented by two coherent states at half-revival time. For certain product states of the atoms, we prove the coherent generation of Greenberger-Horne-Zeilinger states with two atomic qubits and two orthogonal Schr\"odinger cat states as a third qubit. For arbitrary atomic states, we show that discriminating the two states of the field corresponds to different operations in the Bell basis of the atoms. By repeating this process with a second cavity prepared in a phase-shifted coherent state, we demonstrate the implementation of a complete Bell measurement. The experimental feasibility of our protocols is discussed for cavity-QED, circuit-QED, and trapped-ion setups.

arXiv:1811.06176•Physical Review A•Feb 26, 2019•28 citations

Quantum-state mapping between multilevel atoms and cavity light fields

A. S. Parkins, P. Marte, P. Zoller +2 more

A scheme for the preparation of Fock states and general superposition states of the electromagnetic field in a cavity is studied in detail. The scheme uses adiabatic passage in a strongly coupled atom-cavity system to ``map'' atomic ground-state Zeeman coherence onto the cavity-mode field. We model photon-counting and homodyne measurements of the field exiting the cavity and demonstrate the possibility of generating and detecting highly nonclassical states of the field parameter values close to currently realizable experimental values. The adiabatic passage process is also reversible, enabling cavity-mode fields to be mapped onto atomic ground-state Zeeman coherence. Application of this property to the measurement of cavity fields is discussed, with particular consideration given to a possible scheme for quantum measurements of the intracavity photon number.

Physical Review A•Feb 1, 1995•192 citations
This paper contains a theoretical treatment of a scheme for determining phase-dependent features of a single mode of quantized light fields in general states. The proposal involves using a three-level atom, in a cascade configuration, as a detector. The cascade atom, which is on two-photon resonance with the field, is prepared in a coherent superposition of the upper and lower levels, and detection involves measuring the probability of the cascade atom being in the upper level. The results depend on the phase difference between the amplitudes for the field being in N and N + 2 photon states in the number state basis, and are important in describing nonclassical states, such as squeezed and Schrödinger cat states. The analysis is based on a standard dressed atom model approach and a Fourier treatment of the measured signal. The experimental possibilities of realizing this scheme are also discussed.
A simple scheme is presented that allows the generation and detection of nonclassical states of the electromagnetic (em) field with controllable (predetermined) photon-number and phase distributions. It is based on the two-photon resonant interaction of a single em field mode in a high-Q cavity with initially excited atoms crossing the cavity sequentially (one at a time). The sequence duration should be much shorter than the cavity-mode lifetime. Nonclassical states of the field are generated conditionally, by selecting only those sequences wherein each atom is measured to be in the excited state after the interaction. The field distribution resulting from a sequence of N such measurements is peaked about 2N positions in the phase plane, which evolve sinusoidally as a function of the atomic transit times and are therefore simply controlled. When these peaks are chosen not to overlap, the field state constitutes a generalized Schr\"odinger cat. By choosing them to overlap, we can make parts of the field distribution strongly interfere, giving rise to decimation of the photon-number distribution. In particular, this process can prepare Fock states with controlled photon numbers. The generated phase distribution can be detected by monitoring the pattern of revivals in the excitation of a ``probe'' atom.
We put forward a simple, feasible scheme for the preparation and subsequent detection of macroscopic quantum superposition (MQS) states. It is based on the two-photon model which obtains when a cascade of two atomic transitions is resonant with twice the field frequency. The initial conditions amount to a field in a mixed state characteristic of lasers or masers and an excited atom. The MQS is generated by a conditional measurement of the atomic excitation after an interaction time that determines the relative phase of the MQS components. Remarkably, the MQS is subsequently detected and its phase is inferred by measuring the excitation probability of a second, ``probe,'' atom, as a function of its interaction time. The realization of the scheme in the optical domain, using dielectric microspheres, is discussed.
It has been recently shown [1] that, under suitable conditions, the interaction between a three-level atom and the quantized field of a bimodal microcavity may be effectively reduced to the two-photon coupling between a single two-level atom and the electromagnetic field in the resonator. The corresponding Hamiltonian model is characterized by intensity-dependent Stark shifts due to the presence of an intermediate off-resonance atomic level. Assume the cavity field prepared at in an arbitrary state and let an initially excited atom cross the cavity with an appropriately selected velocity. It is possible to show that, exploiting a single conditional measurement of the atomic state immediately after the atom leaves the resonator, the bimodal field is projected into a new state characterized by the same photon number distribution present at More in detail, the experimental scheme we propose makes it possible manipulating only the phases of the initial probability amplitudes of finding a well defined population in the cavity. We prove that the state into which the cavity collapses after a successful atomic measurement is unitarily related to the initial field state and the explicit form of the accomplishing operator is constructed. We wish to remark that, beside its inherent theoretical interest, this simple experimental scheme might also be of relevance in the socalled field of quantum communication [2], where implementing unitary modifications of a quantum state signal represents an issue of topical and central importance. More in general, our proposal provides a systematic procedure for controlling selected properties of a quantum state. We in fact demonstrate that our experimental scheme may be reliably exploited to generate orthogonal states to a prefixed one or to control the squeezing direction.
We present various schemes for measuring the quantum state of a single mode of the electromagnetic field. These involve measuring the photon statistics for the mode before and after an interaction with either one or two two-level atoms. The photon statistics conditioned on the final state of the atoms, for two choices of the initial set of atomic states, along with the initial photon statistics, may be used to calculate the complete quantum state in a simple manner. Alternatively, when one atom is used, two unconditioned sets of photon statistics, each after interaction with a single atom in different initial states, along with the initial photon statistics may be used to calculate the initial state in a simple manner. When the cavity is allowed to interact with just one atom, only pure cavity states which do not contain zeros in the photon distribution may be reconstructed. When two atoms are used we may reconstruct pure states which do not contain adjacent zeros in the photon distribution. Coherent states and number states are among those that may be measured with one-atom interaction, and squeezed states and ‚Schrödinger cats‘ are among those that may be measured with a two-atom interaction.
We introduce a complete Bell measurement on atomic qubits based on two-photon interactions with optical cavities and discrimination of coherent states of light. The dynamical system is described by the Dicke model for two three-level atoms interacting in two-photon resonance with a single mode of the radiation field, which is known to effectively generate a nonlinear two-photon interaction between the field and two states of each atom. For initial coherent states with a large mean photon number, the field state is well represented by two coherent states at half-revival time. For certain product states of the atoms, we prove the coherent generation of Greenberger-Horne-Zeilinger states with two atomic qubits and two orthogonal Schr\"odinger cat states as a third qubit. For arbitrary atomic states, we show that discriminating the two states of the field corresponds to different operations in the Bell basis of the atoms. By repeating this process with a second cavity prepared in a phase-shifted coherent state, we demonstrate the implementation of a complete Bell measurement. The experimental feasibility of our protocols is discussed for cavity-QED, circuit-QED, and trapped-ion setups.
A scheme for the preparation of Fock states and general superposition states of the electromagnetic field in a cavity is studied in detail. The scheme uses adiabatic passage in a strongly coupled atom-cavity system to ``map'' atomic ground-state Zeeman coherence onto the cavity-mode field. We model photon-counting and homodyne measurements of the field exiting the cavity and demonstrate the possibility of generating and detecting highly nonclassical states of the field parameter values close to currently realizable experimental values. The adiabatic passage process is also reversible, enabling cavity-mode fields to be mapped onto atomic ground-state Zeeman coherence. Application of this property to the measurement of cavity fields is discussed, with particular consideration given to a possible scheme for quantum measurements of the intracavity photon number.