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

Acta Physica Sinica

QUANTUM JUMP AND CONTINUOUS MEASUREMENT IN MULTI LEVEL ATOM

Yi Xia

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

Abstract In this paper we investigate the quantum jump in a multi level atom and construct a formal solution to the optical Block equation describing the interaction system of the multi level atom with incident resonant laser.It is proved that pure state analysis theory is no longer applicable to a multi level atom system,so a mixed one is developed,concluding that the resetting density of a multi level atom should be described by mixed state analysis theory.We also discuss the continuous quantum measurement along with quantum jumping in a multi level atom.

Related papers

QUANTUM JUMP AND CONTINUOUS MEASUREMENT IN MULTI-LEVEL ATOM

Yi-Xin Chen, SHANGGUAN WANGZUO, JI DA-REN +1 more

In this paper we investigate the quantum jump in a multi-level atom and construct a formal solution to the optical Block equation describing the interaction system of the multi-level atom with incident resonant laser. It is proved that pure state analysis theory is no longer applicable to a multi-level atom system, so a mixed one is developed, concluding that the resetting density of a multi-level atom should be described by mixed state analysis theory. We also discuss the continuous quantum measurement along with quantum jumping in a multi-level atom.

Acta Physica Sinica•Jan 1, 1999•0 citations

Dressed-state analysis of three-level quantum-jump experiments

Martin Ligare

Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.

Physical Review A•May 1, 1988•14 citations

Quantum state transfer, quantum memory, and quantum networks based on multi-photon processes in cavity QED

Moteb M. Alqahtani, Ghayda AlWaleed Abushawarib, B. M. Garraway

Abstract A method is presented for transfer of a quantum state from one atom to another atom. In this method, we consider the interaction of a multi-mode cavity with a multi-level quantum system and adopt the multi-photon resonance theory for preparing an efficient quantum memory and a quantum network. From the use of effective two- and three-level Hamiltonians, the proper values for interaction times, coupling constants, and detunings are predicted. To examine the sensitivity of the quantum state transfer against decoherence processes, we introduce the quantum-jump approach. Proceeding with this approach leads to a description of the system via wavefunctions instead of density operators and provides simple effective differential equations for obtaining analytic expressions of the probability amplitudes.

Physica Scripta•Dec 1, 2025•0 citations

QUANTUM LASER THEORY AND MEASUREMENT

Murray, Iii Sargent

In Chap. 17 we developed the quantum theory of the laser obtaining in particular expressions for the laser photon statistics and linewidth. In this chapter we discuss and amplify those results in terms of measurement theory. Section 18-1 provides an overview of measurement theory as it applies to the quantum electric field. The discussion leads naturally into a specific discussion of the measurement of photon statistics and the laser linewidth. In Sec. 18-2 a heuristic model of a photodetector is presented with reveals how the photo­ electron statistics resulting from incident radiation is related to the photon statistics of that radiation, t In Sec. 18-3 we discuss the laser linewidth with the use of a simple two level atom beam much like that of Sec. 16-1. Our present discussion utilizes the density matrix technique throughout rather than the density matrix-state vector combination of Sec. 16-1. The laser spectrum “seen” by the atomic beam has, in fact, the same Lorentzian profile given in Sec. 17-3. In Sec. 18-4 the laser linewidth is discussed in terms of a quantum version of the classical correlation function <£(* -f t )E(t)y. In spite of the fact that two time correlations are apparently required, we show that a single time and solutions to the density operator equation of motion are sufficient. This reduction is an example of the so-called Onsager regression hypothesis, which shows how to proceed from single-time to multitime correlation functions.

CRC Press eBooks•Mar 5, 2018•0 citations

Coherent qubit measurement in cavity-transmon quantum systems

Massimo Porrati B, Seth Putterman

A measurement of the time between quantum jumps implies the capability to measure the next jump. During the time between jumps the quantum system is not evolving in a closed or unitary manner. While the wave function maintains phase coherence it evolves according to a non-Hermitian effective Hamiltonian. So under null measurement the timing of the next quantum jump can change by very many orders of magnitude when compared to rates obtained by multiplying lifetimes with occupation probabilities obtained via unitary transformation. The theory developed in 1987 for atomic fluorescence is here extended to transitions in transmon qubits. These systems differ from atoms in that they are read out with a harmonic cavity whose resonance is determined by the state of the qubit. We extend our analysis of atomic fluorescence to this infinite level system by treating the cavity as a quantum system. We find that next photon statistics is highly nonexponential and when implemented will enable faster readout, such as on timescales shorter than the decay time of the cavity. Commonly used heterodyne measurements are applied on timescales longer than the cavity lifetime. The overlap between the next photon theory and the theory of heterodyne measurement which are described according to the stochastic Schr\"odinger equation is elucidated. In the limit of large dispersion the intrinsic error for next jump detection, at short time, tends to zero. Whereas for short-time dyne detection the error remains finite for all values of dispersion.

arXiv:2112.09272•Physical Review A•Jun 22, 2023•0 citations

A Straightforward Introduction to Continuous Quantum Measurement

Jacobs, K, Steck, D A

We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary background material for those new to measurement theory, and describe further various aspects of continuous measurements that should be helpful to those wanting to use such measurements in applications. Specifically, we use the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables, give a tutorial on stochastic calculus, treat multiple observers and inefficient detection, examine a general form of the measurement master equation, and show how the master equation leads to information gain and disturbance. To conclude, we give a detailed treatment of imaging the resonance fluorescence from a single atom as a concrete example of how a continuous position measurement arises in a physical system.

•Nov 6, 2006•262 citations
Abstract In
this paper we investigate the quantum jump in a multi level atom and construct a formal
solution to the optical Block equation describing the interaction system of the multi level atom
with incident resonant laser.It is proved that pure state analysis theory is no longer applicable
to a multi level atom system,so a mixed one is developed,concluding that the resetting density
of a multi level atom should be described by mixed state analysis theory.We also discuss the
continuous quantum measurement along with quantum jumping in a multi level atom.
In this paper we investigate the quantum jump in a multi-level atom and construct a formal solution to the optical Block equation describing the interaction system of the multi-level atom with incident resonant laser. It is proved that pure state analysis theory is no longer applicable to a multi-level atom system, so a mixed one is developed, concluding that the resetting density of a multi-level atom should be described by mixed state analysis theory. We also discuss the continuous quantum measurement along with quantum jumping in a multi-level atom.
Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.
Abstract A method is presented for transfer of a quantum state from one atom to another atom. In this method, we consider the interaction of a multi-mode cavity with a multi-level quantum system and adopt the multi-photon resonance theory for preparing an efficient quantum memory and a quantum network. From the use of effective two- and three-level Hamiltonians, the proper values for interaction times, coupling constants, and detunings are predicted. To examine the sensitivity of the quantum state transfer against decoherence processes, we introduce the quantum-jump approach. Proceeding with this approach leads to a description of the system via wavefunctions instead of density operators and provides simple effective differential equations for obtaining analytic expressions of the probability amplitudes.
In Chap. 17 we developed the quantum theory of the laser obtaining in particular expressions for the laser photon statistics and linewidth. In this chapter we discuss and amplify those results in terms of measurement theory. Section 18-1 provides an overview of measurement theory as it applies to the quantum electric field. The discussion leads naturally into a specific discussion of the measurement of photon statistics and the laser linewidth. In Sec. 18-2 a heuristic model of a photodetector is presented with reveals how the photo­ electron statistics resulting from incident radiation is related to the photon statistics of that radiation, t In Sec. 18-3 we discuss the laser linewidth with the use of a simple two level atom beam much like that of Sec. 16-1. Our present discussion utilizes the density matrix technique throughout rather than the density matrix-state vector combination of Sec. 16-1. The laser spectrum “seen” by the atomic beam has, in fact, the same Lorentzian profile given in Sec. 17-3. In Sec. 18-4 the laser linewidth is discussed in terms of a quantum version of the classical correlation function <£(* -f t )E(t)y. In spite of the fact that two time correlations are apparently required, we show that a single time and solutions to the density operator equation of motion are sufficient. This reduction is an example of the so-called Onsager regression hypothesis, which shows how to proceed from single-time to multitime correlation functions.
A measurement of the time between quantum jumps implies the capability to measure the next jump. During the time between jumps the quantum system is not evolving in a closed or unitary manner. While the wave function maintains phase coherence it evolves according to a non-Hermitian effective Hamiltonian. So under null measurement the timing of the next quantum jump can change by very many orders of magnitude when compared to rates obtained by multiplying lifetimes with occupation probabilities obtained via unitary transformation. The theory developed in 1987 for atomic fluorescence is here extended to transitions in transmon qubits. These systems differ from atoms in that they are read out with a harmonic cavity whose resonance is determined by the state of the qubit. We extend our analysis of atomic fluorescence to this infinite level system by treating the cavity as a quantum system. We find that next photon statistics is highly nonexponential and when implemented will enable faster readout, such as on timescales shorter than the decay time of the cavity. Commonly used heterodyne measurements are applied on timescales longer than the cavity lifetime. The overlap between the next photon theory and the theory of heterodyne measurement which are described according to the stochastic Schr\"odinger equation is elucidated. In the limit of large dispersion the intrinsic error for next jump detection, at short time, tends to zero. Whereas for short-time dyne detection the error remains finite for all values of dispersion.
We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary background material for those new to measurement theory, and describe further various aspects of continuous measurements that should be helpful to those wanting to use such measurements in applications. Specifically, we use the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables, give a tutorial on stochastic calculus, treat multiple observers and inefficient detection, examine a general form of the measurement master equation, and show how the master equation leads to information gain and disturbance. To conclude, we give a detailed treatment of imaging the resonance fluorescence from a single atom as a concrete example of how a continuous position measurement arises in a physical system.