Repeated measurements in quantum mechanics can freeze (the quantum Zeno effect) or enhance (the quantum anti-Zeno effect) the time-evolution of a quantum system. In this paper, we present a general treatment of the quantum Zeno and anti-Zeno effects for arbitrary driven open quantum systems, assuming only that the system-environment coupling is weak. In particular, we obtain a general expression for the effective decay rate of a two-level system subjected to arbitrary driving fields as well as periodic measurements. We demonstrate that the driving fields change the decay rate, and hence the quantum Zeno and anti-Zeno behavior, both qualitatively and quantitatively. We also extend our results to systems consisting of more than one two-level system, as well as a two-level system strongly coupled to an environment of harmonic oscillators, to further illustrate the non-trivial effect of the driving fields on the quantum Zeno and anti-Zeno effects.Repeated measurements in quantum mechanics can freeze (the quantum Zeno effect) or enhance (the quantum anti-Zeno effect) the time-evolution of a quantum system. In this paper, we present a general treatment of the quantum Zeno and anti-Zeno effects for arbitrary driven open quantum systems, assuming only that the system-environment coupling is weak. In particular, we obtain a general expression for the effective decay rate of a two-level system subjected to arbitrary driving fields as well as periodic measurements. We demonstrate that the driving fields change the decay rate, and hence the quantum Zeno and anti-Zeno behavior, both qualitatively and quantitatively. We also extend our results to systems consisting of more than one two-level system, as well as a two-level system strongly coupled to an environment of harmonic oscillators, to further illustrate the non-trivial effect of the driving fields on the quantum Zeno and anti-Zeno effects.

arXiv:2012.15040Scientific ReportsJan 19, 20213 citations

Electromagnetically induced transparency and evolution of a two-level system under a strong chaotic field

Abraham G. Kofman

The present paper treats the electromagnetically induced transparency (EIT), i.e., the absorption spectrum of a weak probe field, near-resonant to a material transition, in the presence of a strong amplitude-phase fluctuating field which couples the upper level of the transition to another excited level. The coupling field is assumed to be chaotic (i.e., a complex Gaussian process with a Lorentzian spectrum) and so strong that the material relaxation and the detuning can be neglected. In addition, we consider the Fourier transform of the spectrum ${U}_{\mathrm{aa}}(t),$ which determines absorption of a probe field with a time-dependent intensity. The quantity ${U}_{\mathrm{aa}}(t)$ equals a diagonal element of the average reduced evolution operator of the two-level system (TLS), coupled by the strong field. As a starting point, we use the stationary, partially averaged stochastic Schr\"odinger equation, which has the form of a set of two second-order differential equations. The theory is developed by combining analytical and numerical approaches. For the most important regime, when the rms Rabi frequency ${V}_{0}$ is much greater than the coupling-field bandwidth $\ensuremath{\nu},$ we obtain scaling relations for the EIT line shape and the TLS evolution. In particular, the absorption at the minimum (i.e., at the resonance frequency) scales as ${\ensuremath{\nu}}^{1/3}{V}_{0}^{\ensuremath{-}4/3},$ whereas the evolution function ${U}_{\mathrm{aa}}(t)$ performs damped oscillations with the decay rate on the order of ${(V}_{0}^{2}\ensuremath{\nu}{)}^{1/3}.$ These results differ significantly from those following from the uncorrelated-jump model. The results of this paper are shown to be applicable to more general models of amplitude-phase fluctuations than the Gaussian-Markovian chaotic field.The present paper treats the electromagnetically induced transparency (EIT), i.e., the absorption spectrum of a weak probe field, near-resonant to a material transition, in the presence of a strong amplitude-phase fluctuating field which couples the upper level of the transition to another excited level. The coupling field is assumed to be chaotic (i.e., a complex Gaussian process with a Lorentzian spectrum) and so strong that the material relaxation and the detuning can be neglected. In addition, we consider the Fourier transform of the spectrum ${U}_{\mathrm{aa}}(t),$ which determines absorption of a probe field with a time-dependent intensity. The quantity ${U}_{\mathrm{aa}}(t)$ equals a diagonal element of the average reduced evolution operator of the two-level system (TLS), coupled by the strong field. As a starting point, we use the stationary, partially averaged stochastic Schr\"odinger equation, which has the form of a set of two second-order differential equations. The theory is developed by combining analytical and numerical approaches. For the most important regime, when the rms Rabi frequency ${V}_{0}$ is much greater than the coupling-field bandwidth $\ensuremath{\nu},$ we obtain scaling relations for the EIT line shape and the TLS evolution. In particular, the absorption at the minimum (i.e., at the resonance frequency) scales as ${\ensuremath{\nu}}^{1/3}{V}_{0}^{\ensuremath{-}4/3},$ whereas the evolution function ${U}_{\mathrm{aa}}(t)$ performs damped oscillations with the decay rate on the order of ${(V}_{0}^{2}\ensuremath{\nu}{)}^{1/3}.$ These results differ significantly from those following from the uncorrelated-jump model. The results of this paper are shown to be applicable to more general models of amplitude-phase fluctuations than the Gaussian-Markovian chaotic field.

Physical Review AFeb 13, 20014 citations

Field Matter Coupling and Two-Level Systems

Springer series on atomic, optical, and plasma physicsJan 1, 20080 citations

Field Matter Coupling and Two-Level Systems

Frank Großmann

Graduate texts in physicsJan 1, 20130 citations

The Zeno and anti-Zeno effects: studying modified decay rates for spin-boson models with both strong and weak system-environment couplings

Irfan Javed, Mohsin Raza

In this paper, we look into what happens to a quantum system under repeated measurements if system evolution is removed before each measurement is performed. Beginning with investigating a single two-level system coupled to two independent baths of harmonic oscillators, we move to replacing it with a large collection of such systems, thereby invoking the large spin-boson model. Whereas each of our two-level systems interacts strongly with one of the aforementioned baths, it interacts weakly with the other. A polaron transformation is used to make it possible for the problem in the strong coupling regime to be treated with perturbation theory. We find that the case involving a single two-level system exhibits qualitative and quantitative differences from the case involving a collection of them; however, the general effects of strong and weak couplings turn out to be the same as those in the presence of system evolution, something which allows us to establish that system evolution has no practical bearing on any of these effects.In this paper, we look into what happens to a quantum system under repeated measurements if system evolution is removed before each measurement is performed. Beginning with investigating a single two-level system coupled to two independent baths of harmonic oscillators, we move to replacing it with a large collection of such systems, thereby invoking the large spin-boson model. Whereas each of our two-level systems interacts strongly with one of the aforementioned baths, it interacts weakly with the other. A polaron transformation is used to make it possible for the problem in the strong coupling regime to be treated with perturbation theory. We find that the case involving a single two-level system exhibits qualitative and quantitative differences from the case involving a collection of them; however, the general effects of strong and weak couplings turn out to be the same as those in the presence of system evolution, something which allows us to establish that system evolution has no practical bearing on any of these effects.

arXiv:2012.05911Dec 10, 20200 citations

{U}_{\mathrm{aa}}(t),

which determines absorption of a probe field with a time-dependent intensity. The quantity

{U}_{\mathrm{aa}}(t)

equals a diagonal element of the average reduced evolution operator of the two-level system (TLS), coupled by the strong field. As a starting point, we use the stationary, partially averaged stochastic Schr\"odinger equation, which has the form of a set of two second-order differential equations. The theory is developed by combining analytical and numerical approaches. For the most important regime, when the rms Rabi frequency

{V}_{0}

is much greater than the coupling-field bandwidth $\ensuremath{\nu},$ we obtain scaling relations for the EIT line shape and the TLS evolution. In particular, the absorption at the minimum (i.e., at the resonance frequency) scales as ${\ensuremath{\nu}}^{1/3}{V}_{0}^{\ensuremath{-}4/3},$ whereas the evolution function

{U}_{\mathrm{aa}}(t)

performs damped oscillations with the decay rate on the order of ${(V}_{0}^{2}\ensuremath{\nu}{)}^{1/3}.$ These results differ significantly from those following from the uncorrelated-jump model. The results of this paper are shown to be applicable to more general models of amplitude-phase fluctuations than the Gaussian-Markovian chaotic field.