Pure two-atom squeezed state in spontaneous emission from two non-identical atoms

We calculate the stationary state of the system of two non-identical two-level atoms driven by a finite-bandwidth two-mode squeezed vacuum. It is well known that two identical two-level atoms driven by a broadband squeezed vacuum may decay to a pure state, called the pure two-atom squeezed state, and that the presence of the antisymmetric state can change its purity. Here, we show that for small interatomic separations the stationary state of two non-identical atoms is not sensitive to the presence of the antisymmetric state and is the pure two-atom squeezed state. This effect is a consequence of the fact that in the system of two non-identical atoms the antisymmetric state is no longer the trapping state. We also calculate the squeezing properties of the emitted field and find that the squeezing spectrum of the output field may exhibit larger squeezing than that in the input squeezed vacuum. Moreover, we show that squeezing in the total field attains the optimum value which can ever be achieved in the field emitted by two atoms.

A squeezed state holomorphic phase space representation of equations of motion

A mapping scheme is presented which takes quantum operators associated to bosonic degrees of freedom into complex phase space integral kernel representatives. The procedure consists of using the Schrödinger squeezed state as the starting point for the construction of the integral mapping kernel which, due to its inherent structure, is suited for the description of second quantized operators. Products and commutators of operators have their representatives explicitly written which reveal new details when compared to the usual q-p phase space description. The classical limit of the equations of motion for the canonical pair q-p is discussed in connection with the effect of squeezing the quantum phase space cellular structure. © 1993.

Squeezed states, generalized Hermite polynomials and pseudo-diffusion equation

We show that the wavefunctions 〈pq; λ|n〈, of the harmonic oscillator in the squeezed state representation, have the generalized Hermite polynomials as their natural orthogonal polynomials. These wavefunctions lead to generalized Poisson Distribution Pn(pq;λ), which satisfy an interesting pseudo-diffusion equation: ∂Pnp,q;λ) ∂λ= 1 4 [ ∂2 ∂p2-( 1 λ2) ∂2 ∂q2]P2(p,q;λ), in which the squeeze parameter λ plays the role of time. Th entropies Sn(λ) have minima at the unsqueezed states (λ=1), which means that squeezing or stretching decreases the correlation between momentum p and position q. © 1992.

Equivalence between two-mode spin squeezed states and pure entangled states with equal spin

We prove that a pure entangled state of two subsystems with equal spin is equivalent to a two-mode spin-squeezed state under local operations except for a set of bipartite states with measure zero, and provide a counterexample to the generalization of this result to two subsystems of unequal spin.

Numerical investigation of the quantum fluctuations of optical fields transmitted through an atomic medium

We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field, and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving-field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific to (Zeeman) multilevel configurations are identified.

Interference in hyperbolic space

The interference in a phase space algorithm of Schleich and Wheeler [Nature 326, 574 (1987)] is extended to the hyperbolic space underlying the group SU(1,1). The extension involves introducing the notion of weighted areas. Analytic expressions for the asymptotic forms for overlaps between the eigenstates of the generators of su(1,1) thus obtained are found to be in excellent agreement with the numerical results.[S1050-2947(98)08602-8].

Polarization squeezing and continuous-variable polarization entanglement

A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.

Optical experiments beyond the quantum limit: Squeezing entanglement and teleportation

Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.

An analog model for quantum lightcone fluctuations in nonlinear optics

We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable. © 2012 Elsevier Inc.

Densidade de energia e força de radiação sobre fronteiras em movimento para estados arbitrários do campo: aplicação ao estado coerente

No presente trabalho foi considerado um campo escalar real não massivo em um espaço-tempo bidimensional, satisfazendo à condição de fronteira Dirichlet ou Neumann na posição instantânea de uma fronteira em movimento. Para uma lei de movimento relativística, foi mostrado que as condiçõoes de fronteira Dirichlet e Neumann produzem a mesma força de radiação sobre um espelho em movimento quando o estado inicial do campo é invariante sobre translações temporais. Obtemos as fórmulas exatas para a densidade de energia do campo e da força de radiação na fronteira para os estados de vácuo, coerente e comprimido. No limite não-relativistico, os resultados obtidos coincidem com os encontrados na literatura. Também foi investigado o campo dentro de uma cavidade oscilante. Considerando as condiçõoes de fronteira Neumann e Dirichlet, escreveu-se a fórmulas exata para a densidade de energia dentro de uma cavidade não-estática, para um estado inicial arbitrário do campo. Tomando como base a equação de Moore, nós calculamos recursivamente a densidade de energia e investigamos a evolução temporal da densidade de energia para o estado coerente do campo.

Spin coherent states in NMR quadrupolar system: experimental and theoretical applications

Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudonuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo- NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: (i) the free evolution of the NMR quadrupolar system and, by analogy with the evolution of the NMR quadrupolar system, that of (ii) single-mode and (iii) two-mode Bose-Einstein Condensate like system. By means of these analogies, we derive, through spin angular momentum operators, results equivalent to those presented in the literature for orbital angular momentum operators. The pseudo-NSCS description is a starting point to introduce the spin squeezed state and quantum metrology into nuclear spin systems of liquid crystal or solid matter.

Gaussian quantum operator representation for bosons

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.

Tomographic readout of an opto-mechanical interferometer

The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. Full information of the state of light can only be gathered by a tomographic measurement. Here we demonstrate a tomographic interferometer readout by measuring arbitrary quadratures of the light field exiting a Michelson-Sagnac interferometer that contains a thermally excited high-quality silicon nitride membrane. A readout noise of 1.9 x 10(-16) mHz(-1/2) around the membrane's fundamental oscillation mode at 133 kHz has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.

Satisfying the Einstein-Podolsky-Rosen criterion with massive particles

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.

Anomalous resonance fluorescence and dressed-state inversion by squeezed light in a Fabry-Perot microcavity

It has been suggested that phased atomic decay in a squeezed vacuum could be detected in the fluorescence spectrum emitted from a driven two-level atom in a cavity. Recently, the existence of other very distinctive features in the fluorescence spectra arising from the nonclassical features of the squeezed vacuum has been reported. In this paper, we investigate the possibility of experimental observation of these spectra. The main obstacle to the experimentalist is ensuring an effective squeezed-vacuum-atom coupling. To overcome this problem we propose the use of a Fabry-Perot microcavity. The analysis involves a consideration of the three-dimensional nature of the electromagnetic held, and the possibility of a mismatch between the squeezed and cavity modes. The problem of squeezing bandwidths is also addressed. We show that under experimentally realistic circumstances many of the spectral anomalies predicted in free space also occur in this environment. In addition, we report large population inversions in the dressed states of the two-level atom. [S1050-2947(98)02301-4].