Quantum Optical States Research Articles

Violation of Bell’s inequalities and two-mode quantum-optical state measurement

Violation of Bell’s inequalities and two-mode quantum-optical state measurement

Discretized representations of harmonic variables by bilateral Jacobi operators

Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q‐oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non‐interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.

Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms

We consider a class of states in an ensemble of two-level atoms: a superposition of two distinct atomic coherent states, which can be regarded as atomic analogues of the states usually called Schrodinger cat states in quantum optics. According to the relation of the constituents we define polar and nonpolar cat states. The properties of these are investigated by the aid of the spherical Wigner function. We show that nonpolar cat states generally exhibit squeezing, the measure of which depends on the separation of the components of the cat, and also on the number of the constituent atoms. By solving the master equation for the polar cat state embedded in an external environment, we determine the characteristic times of decoherence, dissipation and also the characteristic time of a new parameter, the non-classicality of the state. This latter one is introduced by the help of the Wigner function, which is used also to visualize the process. The dependence of the characteristic times on the number of atoms of the cat and on the temperature of the environment shows that the decoherence of polar cat states is surprisingly slow.

Dressed states of a two component Bose-Einstein condensate

A condensate with two internal states coupled by external electromagnetic radiation, is described by coupled Gross Pitaevskii equations, whose eigenstates are analogous to the dressed states of quantum optics. We solve for these eigenstates numerically in the case of one spatial dimension, and explore their properties as a function of system parameters. In contrast to the quantum optical case, the condensate dressed states exhibit spatial behaviour which depends on the system parameters, and can be manipulated by changing the cw external field.

Theory of dressed states in quantum optics

The dual Dyson series [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both Dyson series and its dual, through renormalization group methods to remove secular terms from the perturbation series, give the opportunity of a full study of the solution of the Schr\"{o}dinger equation in different ranges of the parameters of the given hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to exploit the method at the best, a study is accomplished of the well-known Jaynes-Cummings model in the rotating wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is needed to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.

Transition probabilities between quasifree states

We obtain a general formula for the transition probabilities between any state of the C* algebra of the canonical commutation relations (CCR-algebra) and a squeezed quasifree state (Theorem III.1). Applications of this formula are made for the case of multimode thermal squeezed states of quantum optics using a general canonical decomposition of the correlation matrix valid for any quasifree state. In the particular case of a one-mode CCR-algebra we show that the transition probability between two quasifree squeezed states is a decreasing function of the geodesic distance between the points of the upper half-plane representing these states. In the special case of the purification map it is shown that the transition probability between the state of the enlarged system and the product state of real and fictitious subsystems can be a measure for the entanglement.

Hierarchies of non-classical states in quantum optics

The conventional separation of states of the quantised radiation field into “classical” and “nonclassical” types is expressed in a dual operator form and then refined. This is based on new features of the normal ordering rule for passage from classical to quantum dynamical variables. The cases of single and two-mode radiation fields are discussed

Nonclassical Field States in Quantum Optics and Particle Physics

The primary aim of the present paper is to draw the attention of particle physicists to new developments in studying squeezed and correlated states of the electromagnetic field, and those working on the latest developments to new findings about multiplicity distributions and other specific effects in quantum chromodynamics. New types of nonclassical states used in quantum optics such as squeezed states, correlated states, and even and odd coherent states (Schrodinger cat states) for one-mode and multimode interactions are reviewed. Their distribution functions are analyzed according to the method first used for multiplicity distributions in high-energy particle interactions. The phenomenon of oscillations of particle distribution functions of squeezed fields is described and related to the phenomenon of oscillations of cumulant moments of some distributions for squeezed and correlated field states. Possible extension of the method to fields different from the electromagnetic field (gluons, pions, etc.) is conjectured, and some predictions of specific effects in nucleus-nucleus interactions at high energies are presented.

Generation and preservation of coherence in dissipative quantum optical environments

We discuss the decay and decoherence of nonclassical states in quantum optics coupled to zero-temperature heat baths, and contrast ensemble behaviour with that of individual realizations. We show how nonclassical states are highly sensitive to dissipation in a number of cases, but present an example of how dissipation can be used to generate nonclassical states.

Wigner distribution for density of states in quantum optics

We demonstrate the occurrence of the well-known Wigner distribution for density of states, which arises commonly in nuclear physics, in a class of problems in quantum optics. We show how such a distribution can be probed, and analyze the effects of dissipation on this distribution, one of which is to make the underlying random matrix non-Hermitian.

Two-mode quantum-optical state measurement: Sampling the joint density matrix.

Two-mode quantum-optical state measurement: Sampling the joint density matrix.

Quantum optical spin-glass state of impurity two-level atoms in a photonic band gap.

Quantum optical spin-glass state of impurity two-level atoms in a photonic band gap.

Squeezing of a Focused Acoustic Beam and Acoustic Microscopy of Anisotropic Media

The concept of squeezing in quantum optics is applied to focused acoustic beam evaluation for the first time. Mathematical equivalence between coherent and squeezed states in quantum optics and angular spectra in various acoustical imaging schemes is derived and discussed. The squeezing operation, which deforms or controls pairs of physical quantities, is defined to evaluate focused acoustic beam quality from a unified point of view, especially in the measurement of anisotropic materials. Furthermore, the concept of the “vector figure of merit” is introduced, which describes both the resolution of focusing and the ability to measure the anisotropy of materials.

Loop coherent states and photon localizability

Loop states in quantum optics and their 1-1 correspondence with states in Fock space are described. Owing to their natural encoding of geometrical information and close relation to coherent states it is proposed that a certain subclass of loop coherent states may be used as a probe for localization of photon states.

Lie-algebra methods in quantum optics: The Liouville-space formulation.

Lie-algebra methods for investigating quantum optical systems are presented within the framework of the Liouville-space formulation. The generalized decomposition formulas for exponential functions of the generators of su(2) and su(1,1) Lie algebras are derived and their expectation values are calculated for typical states in quantum optics. The general procedure for using Lie algebras in the Liouville space to treat quantum optical processes is given in terms of generalized decomposition formulas and their use is demonstrated by calculating the absorption line shape and photon echo signal in a localized electron-phonon system. It is also shown that the photon-counting probability can be calculated by using the su(1,1) Lie algebra and that the electron-counting probability can be calculated by using the su(2) Lie algebra. The su(1,1) Lie algebra is also used to investigate a quantum-nondemolition measurement of photon number in the four-wave-mixing model.

Minimum-uncertainty states, a two-photon system, and quantum-group symmetry.

We provide a model for a two-photon system that possesses quantum-group symmetry. The quadrature-phase amplitudes of the model are defined in terms of deformed oscillator operators. We emphasize the investigation of the most general minimum-uncertainty states, i.e., coherent states and squeezed states, for the quadrature-phase amplitudes alpha1 and alpha2. We show that the squeezed states of the two-photon quantum optics are simultaneous eigenvectors of the operators A+ and A- with eigenvalues a+ and a-, respectively. For an important subset of the squeezed states, the expectation values and variances of relevant operators are given explicitly.

Squeezed boson states in condensed matter.

The possibility of the existence of squeezed states in interacting-boson condensed-matter systems is studied. These states are intimately related to the Bogoliubov and Valatin-Butler wave functions, and they are constructed as a possible ground state for the attractive-interaction Bose problem (AIBP) in a lattice, in which pair states can be formed. The pair ground state is constructed as variational many-body wave function for the AIBP by exploring the analogies with the dynamically generated photon squeezed states of quantum optics. The possible existence of these boson squeezed states is discussed in the context of biexcitons. In order to characterize the statistical properties of the pair (squeezed) state, the boson-field amplitude fluctuations, number probability distribution, and the second-order correlation function are calculated.

Squeezed states of an optical field in a distributed-feedback system under Bragg resonance conditions

An analysis is made of a new method of creating optical quantum states and of a system for controlling these states by dynamic diffraction in a spatially periodic structure. The process involves energy exchange between waves with fixed phase parameters under Bragg diffraction conditions.

A large-scale puzzle

A large-scale puzzle

Thermal counterparts of nonclassical states in quantum optics.

Finite-temperature generalizations of the important, special families of states in quantum optics are constructed using thermofield dynamics. Fermionic coherent states, fermionic squeezed states, and their thermalized counterparts are also constructed. It is shown that all these states possess a generalized thermal annihilation operator, for which these are eigenstates. Typical correlation functions for these states at finite temperature are evaluated.