arXiv subjects
Publications and source records attributed to V. V. Dodonov.
This is a brief review of different aspects of the so-called Dynamical Casimir Effect and the proposals aimed at its possible experimental realizations. A rough classification of these proposals is given and important theoretical problems are pointed out.
Asymptotical formulas for the photon distribution function of a quantum oscillator with time-dependent frequency and damping coefficients, interacting with a thermal reservoir, are derived in the case of a large mean number of quanta. Different regimes of excitation of an initial thermal state with an arbitrary temperature are considered. New formulas are used to predict the statistical properties of the electromagnetic field created in the experiments on the Dynamical Casimir Effect which are now under preparation.
We propose an experimental scheme to probe the form of one-count operation used in the theory of continuous photodetection in cavities. Two main steps are: 1) an absorption of a single photon by an atom passing through a high-Q cavity containing electromagnetic field in a thermal or coherent state, 2) a subsequent measurement of the photon statistics in the new field state arising after the photon absorption. Then comparing the probabilities of finding 0 and 1 photons in the initial and final states of the field, one can make conclusions on the form of the one-count operation. This method can be readily applied in the microwave cavity QED with present technology.
We examine some aspects of the continuous photodetection model for photocounting processes in cavities. First, we work out a microscopic model that describes the field-detector interaction and deduce a general expression for the Quantum Jump Superoperator (QJS), that shapes the detector's post-action on the field upon a detection. We show that in particular cases our model recovers the QJSs previously proposed ad hoc in the literature and point out that by adjusting the detector parameters one can engineer QJSs. Then we set up schemes for experimental verification of the model. By taking into account the ubiquitous non-idealities, we show that by measuring the lower photocounts moments and the mean waiting time one can check which QJS better describes the photocounting phenomenon.
We discuss the quantum jump operation in an open system, and show that jump super-operators related to a system under measurement can be derived from the interaction of that system with a quantum measurement apparatus. We give two examples for the interaction of a monochromatic electromagnetic field in a cavity (the system) with 2-level atoms and with a harmonic oscillator (representing two different kinds of detectors). We show that derived quantum jump super-operators have `nonlinear' form which depends on assumptions made about the interaction between the system and the detector. A continuous transition to the standard Srinivas--Davies form of the quantum jump super-operatoris shown.
We study the back-action of a single photon detector on the electromagnetic field upon a photodetection by considering a microscopic model in which the detector is constituted of a sensor and an amplification mechanism. Using the quantum trajectories approach we determine the Quantum Jump Superoperator (QJS) that describes the action of the detector on the field state immediately after the photocount. The resulting QJS consists of two parts: the bright counts term, representing the real photoabsorptions, and the dark counts term, representing the amplification of intrinsic excitations inside the detector. First we compare our results for the counting rates to experimental data, showing a good agreement. Then we point out that by modifying the field frequency one can engineer the form of QJS, obtaining the QJS's proposed previously in an ad hoc manner.
Some non-ideal effects as non-unit quantum efficiency, dark counts, dead time and cavity losses that occur in experiments are incorporated within the continuous photodetection model by using the analytical quantum trajectories approach. We show that in standard photocounting experiments the validity of the model can be verified, and the formal expression for the quantum jump superoperator can also be checked.
We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an environment can be simulated by two classical stochastic forces. This family is determined by three time-dependent correlation functions (besides the frequency and damping coefficients), and it includes as special cases the known master equations, whose dissipative part is bilinear with respect to the operators of coordinate and momentum.
We study the influence of fluctuations in periodic motion of boundaries of an ideal three-dimensional cavity on the rate of photon generation from vacuum due to the nonstationary Casimir effect.
We are modifying some aspects of the continuous photodetection theory, proposed by Srinivas and Davies [Optica Acta 28, 981 (1981)], which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the `annihilation' and `creation' operators that enter in the photocount superoperators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to Srinivas and Davies precepts, but also avoids some weird result appearing when previous definitions are used.
We introduce a simple measure of "classicality" of pure and mixed quantum states as a maximum value of the Hilbert-Schmidt "scalar products" between the renormalized statistical operators of the state concerned and all displaced thermal states. Choosing Fock states as the reference set, we introduce the measure of "anticlassicality". Both measures are illustrated for the Fock, coherent phase, and generic mixed Gaussian states. Gaussian states are shown to be the closest to thermal states possessing the same degree of quantum purity. On the contrary, Fock states appear to be more close to mixed thermal states than to pure coherent states.
We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a possibility of using the Fokker-Planck equation to describe this evolution. Studying different interaction Hamiltonians, we show that unambiguous reduction to the Fokker-Planck equation is possible only within the framework of the so called rotating-wave approximation. As special cases we consider in detail the evolution of two coupled oscillators and relaxation of a charged oscillator in a uniform magnetic field.
We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropic coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered: a three-dimensional cavity possessing eigenfrequencies $ω_3=3ω_1$, whose wall oscillates at the frequency $ω_w=2ω_1$, and a one-dimensional (Fabry--Perot) cavity with an equidistant spectrum $ω_n= nω_1$, when the distance between perfect mirrors oscillates at the frequencies $ω_1$ and $2ω_1$. The behaviour of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except for some specific situations, where the covariance entanglement coefficient, based on traces of covariance submatrices, seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field are considered: vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states.
An asymmetric nature of the boson `destruction' operator $\hat{a}$ and its `creation' partner $\hat{a}^{\dagger}$ is made apparent by applying them to a quantum state $|ψ>$ different from the Fock state $|n>$. We show that it is possible to {\em increase} (by many times or by any quantity) the mean number of quanta in the new `photon-subtracted' state $\hat{a}|ψ>$. Moreover, for certain `hyper-Poissonian' states $|ψ>$ the mean number of quanta in the (normalized) state $\hat{a}|ψ>$ can be much greater than in the `photon-added' state $\hat{a}^{\dagger}|ψ> $. The explanation of this `paradox' is given and some examples elucidating the meaning of Mandel's $q$-parameter and the exponential phase operators are considered.
We study the peculiarities of the nonstationary Casimir effect (creation of photons in cavities with moving boundaries) in the special case of two resonantly coupled modes with frequencies $ω_0$ and $(3Δ)ω_0$, parametrically excited due to small amplitude oscillations of the ideal cavity wall at the frequency $2ω_0(1δ)$ (with $|δ|,|Δ|\ll 1$). The effects of thermally induced oscillations in time dependences of the mean numbers of created photons and the exchange of quantum purities between the modes are discovered. Squeezing and photon distributions in each modes are calculated for initial vacuum and thermal states. A possibility of compensation of detunings is shown.
This is a review of publications on classical and quantum electrodynamics in cavities with moving boundaries (in the quantum case this subject is labeled frequently as "nonstationary Casimir effect" or "dynamical Casimir effect"), from 1921 to October of 2000, with an emphasis on analytical results related to cavities with resonantly oscillating boundaries.
We introduce the quantitative measures characterizing the rates of decoherence and thermalization of quantum systems. We study the time evolution of these measures in the case of a quantum harmonic oscillator whose relaxation is described in the framework of the standard master equation, for various initial states (coherent, `cat', squeezed and number). We establish the conditions under which the true decoherence measure can be approximated by the linear entropy $1-{Tr}\hatρ^2$. We show that at low temperatures and for highly excited initial states the decoherence process consists of three distinct stages with quite different time scales. In particular, the `cat' states preserve 50% of the initial coherence for a long time interval which increases logarithmically with increase of the initial energy.
We discuss the problem of the information transfer (exchange of states configuration) between two interacting quantum systems along their evolution in time. We consider the specific case of two modes of the electromagnetic field with rotating wave coupling interaction (up-conversion in a nonlinear crystal). We verify that for certain initial states of the fields the swapping of state configuration occurs with conservation of the mean energy of each mode (without energy transfer), characterising thus pure information flow.