Squeezed states of a particle in magnetic field

For a charged particle in a homogeneous magnetic field, we construct stationary squeezed states which are eigenfunctions of the Hamiltonian and the non-Hermitian operator , and Ŷ being the coordinates of the Larmor circle center and Φ is a complex parameter. In the family of the squeezed states, the quantum uncertainty in the Larmor circle position is minimal. The wave functions of the squeezed states in the coordinate representation are found and their properties are discussed. Besides, for arbitrary gauge of the vector potential we derive the symmetry operators of translations and rotations. Fiz. Tverd. Tela (St. Petersburg) 40, 1405–1412 (August 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Squeezed states and quantum chaos

We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos. Zh. éksp. Teor. Fiz. 113, 111–127 (January 1998)     

Squeezed states in two-phonon devices

New variables called two-mode quadrature-phase amplitudes are used in order to analyze squeezing in two-phonon devices. The Fokker-Planck equation obtained for two-mode quasiprobability distributions presents a diffusion matrix independent of the non-linear coupling and with non-negative eigenvalues. Assuming that the initial state is a two-mode coherent state, the uncertainties in the two-mode quadrature-phase amplitudes have been obtained, and the dependence of squeezing in the non-linear coupling, the pumping phase and the modulation frequency has been studied.     

Squeezed states and Helmholtz spectra

The “classical interpretation” of the wave function ψ(x) reveals an interesting operational aspect of the Helmholtz spectra. It is shown that the traditional Sturm-Liouville problem contains the simplest key to predict the squeezing effect for charged particle states.     

Preparation and decoherence of superpositions of electromagnetic field states

In a recent experiment the progressive decoherence of a mesoscopic superposition of two coherent field states in a high-Q cavity, known as Schr?dinger cat state, has been measured for the first time [Brune et al., Phys. Rev. Lett. 77, 4887 (1996)]. Here, the full master equation governing the coupled dissipative dynamics of the atom-field system studied in the experiment is formulated and solved numerically for the experimental parameters. The model simulated avoids the approximations underlying an analytically solvable model which is based on a harmonic expansion of the energies of the dressed atomic states and on a treatment of their dynamics within the adiabatic approximation. In particular, the numerical simulations reveal that the coupling of the cavity field mode to its environment causes important decoherence effects already during the initial preparation phase of the Schr?dinger cat state. This phenomenon is investigated in detail with the help of a measure for the purity of states. Moreover, the Hilbert-Schmidt distance of the intended target state, the Schr?dinger cat, to the state that is actually prepared in the experiment is determined. Received 13 September 2000 and Received in final form 22 December 2000     

Phase Transitions of Thermal Squeezed states

By using thermo field dynamics, we studied the phase transitions of thermal squeezed states. Two critical points are obtained in certain cases. They correspond to the transitions from thermal squeezed state to pure squeezed state and to thermal state respectively.     

Squeezed states in the Jaynes-Cummings model

It is shown that squeezed states of the electromagnetic field are obtained in the Jaynes-Cummings model of an atomic transition coupled to a single mode, quantized electromagnetic field.     

Squeezed states of light as self-similar structures

A new approach to investigating a broad class of dynamic states for a quantum oscillator is suggested. It is based on an invariant transformation of the equation to a new time determined by the quantum dispersion of the corresponding state. The squeezed states of a quantum system generated by the ground-state wave function are constructed. In coordinate representation, these states are described by a self-similar wave function localized near a classical trajectory. The statistics of the squeezed state of light is analyzed in the single-mode approximation. The parametric excitation of squeezed states for a quantum harmonic oscillator is considered.     

Squeezed states in direct and coherent detection

With reference to squeezed states, we analyse the noise performances of the basic detection schemes in fibre telecommunications and interferometry. We have developed a semiclassical approach that allows us to translate the quantum mechanical formalism into synthetic expressions and rules only involving directly measurable physical quantities. As a result, we find that in the telecommunication field squeezed states do not allow significant improvements in system performances: in practice, the signal-to-noise ratio cannot be increased in standard detection schemes, both direct and coherent, by squeezing either the signal (because of propagation losses) or by the local oscillator. On the contrary, a significant improvement can be obtained in interferometric measurements if squeezed vacuum is coupled into the normally unused beamsplitter port.     

Squeezed states and uncertainty relations since 1991

A brief review of the history of ten workshops/conferences on “Squeezed States and Uncertainty Relations” and main achievements in the related fields of quantum physics for the period from 1991 to 2007 are presented.     

Entangled spin states of a Bose condensate in an electromagnetic field

We consider the formation of entangled quantum states for an atomic Bose condensate interacting with an external electromagnetic field in a single-particle state under conditions of change in various regimes for exchange interaction processes. These states of the Bose system have high phase coherence and are accompanied by the generation of squeezed states of a new type in terms of the parameters defined by a combination of transition operators for the condensate atoms and external-field photons with an appropriate polynomial deformation of the algebra SU(2). We show that localized quantum structures corresponding to stable elementary excitations of the atoms and the field in the condensate can be formed in principle. We also analyze the purely quantum effects of collapse and revival for the level populations of the Bose condensate and the change in atomic statistics as well as determine the conditions for the formation of superstructure of these unsteady states for the Bose system.     

Squeezed states parametrized by elements of noncommutative algebras

By analogy with the conventional (q=1) case, a squeezed vacuum state for theq-bosonic oscillator is constructed. It can be shown that this obeys quantum noise relations similar to those found in the undeformed state. Using the unitary displacement operator for theq-boson algebra, we show that it is possible to construct aq-squeezed state which is parameterised by elements of a noncommutative algebra. These states satisfy the Robertson-Schrödinger Uncertainty Relation and can be generalised toq-analogues of correlated coherent states.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.One of the authors (RJM) would like to thank the organizers of this colloquium for giving him the opportunity to attend this meeting. He would also like to thank the Carnegie Trust for support in travelling expenses.     

Squeezed states in resonance fluorescence of two interacting atoms

The possible existence of so-called “squeezed” states in two-atom resonance fluorescence is discussed in Lehmberg's master equation approach. It is shown that squeezing strongly depends on interatomic separations r₁₂. For large r₁₂ one of the quadrature components is squeezed, and as r₁₂ decreases its squeezing decreases in order to appear in the other quadrature component for certain value of r₁₂. For very small r₁₂ fluctuations in both components tend to zero.     

Squeezed thermal spin states of magnons in the ferromagnet

In this paper, we discuss squeezed thermal spin states of magnons that are described by the Heisenberg Hamiltonian in the ferromagnet, in which the magnon system possesses a new kind of quasiparticle, which we call ferromagnon, i.e. a “dressed” quasi-particle obtained from the magnons by a Bogoliubov-Valatin transformation . Generally, the mass and noise properties of ferromagnons possess potentially important and novel effects in condensed matter physics, which have extensive application in the fields of science and technology. Moreover, it is convenient to introduce the Holstein-Primakoff method, in order to take into account the nonlinear interaction among spin waves. At last we describe the quantum fluctuations of spin-components in the squeezed thermal spin states of magnons and their temperature-dependence. Below some temperature, the squeezed thermal spin states of ferromagnons show squeeze effect.     

Squeezed states of long-lived terahertz vibrations in quantum dots

Quantum dots based on materials with long-lived terahertz vibrations are studied. It is shown that squeezed states of such vibrations can result in microwave-frequency modulation of the optical radiation absorbed at electronic transitions in quantum dots. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 199–200 (25 January 1997)     

Study of electromagnetic field surface states in photonic crystals using the finite-difference method

Bulletin of the Lebedev Physics Institute - The properties of electromagnetic field surface states in globular photonic crystals are analyzed using numerical solution of Maxwell equations by the...