We study the effect of photothermal fluctuations on squeezed states of light through the photo-refractive effect and thermal expansion in a degenerate optical parametric oscillator (OPO). We also discuss the effect of the photothermal noise in various cases and how to minimize its undesirable consequences. We find that the photothermal noise in the OPO introduces a significant amount of noise on phase squeezed beams, making them less than ideal for low-frequency applications such as gravitational wave (GW) interferometers, whereas amplitude squeezed beams are relatively immune to the photothermal noise and may represent the best choice for application in GW interferometers.

The second-order perturbation corrections to the energy computed using the optimized effective potential (OEP) arising from single-particle excitations are computed explicitly for a number of closed-shell atoms. It is found that almost all of the difference between the Hartree-Fock energy and the OEP energy is recovered in second order.

Dipole interference is studied when atomic systems are coupled to classical electromagnetic fields. The interaction between the dipoles and the classical fields induces a time-varying Aharonov-Casher phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be observable and almost as large as the corresponding one for coherent electrons. We analyze different trajectories in order to show the dependence of the decoherence factor with the velocity of the particles.

We characterize violation of Clauser-Horne-Shimony-Holt (CHSH) inequalities for mixed two-qubit states by their mixedness and entanglement. The class of states that have maximum degree of CHSH violation for a given linear entropy is also constructed.

A pair of charge qubits in a random electromagnetic environment is studied, using the description of the random dynamics of its pure-state vector as given by quantum-state diffusion theory. It is shown by numerical computations that the pure-state dynamics provides a more detailed description than the density-matrix picture of the main effects such as phase dumping and depolarization.

We investigate collective oscillations of nondegenerate clouds of ${}^{87}\mathrm{Rb}$ atoms as a function of density in an elongated magnetic trap. For the low-lying $M=0$ monopole-quadrupole shape oscillation we measure the oscillation frequencies and damping rates. At the highest densities the mean free path is smaller than the axial dimension of the sample, which corresponds to collisionally hydrodynamic conditions. This allows us to cover the crossover from the collisionless to the hydrodynamic regime. The experimental results show good agreement with theory. We also analyze the influence of trap anharmonicities on the oscillations in relation to observed temperature dependencies of the dipole and quadrupole oscillation frequencies. We present convenient expressions to quantify these effects.

The BCS-to-BEC crossover, as well as the nature of Cooper pairs, in superconducting and Fermi superfluid media is studied from the exact ground state wave function of the reduced BCS Hamiltonian. As the strength of the interaction increases, the ground state continuously evolves from a mixed system of quasifree fermions and pair resonances (BCS), to pair resonances and quasibound molecules (pseudogap), and finally to a system of quasibound molecules (BEC). A single unified scenario arises where the Cooper-pair wave function has a unique functional form. Several exact analytic expressions such as the binding energy and condensate fraction are derived. We compare our results with recent experiments in ultracold atomic Fermi gases.

We report results of numerical simulations on multiple-soliton generation and soliton energy quantization in a soliton fiber ring laser passively mode locked by using the nonlinear polarization rotation technique. We found numerically that the formation of multiple solitons in the laser is caused by a peak-power-limiting effect of the laser cavity. It is also the same effect that suppresses the soliton pulse collapse, an intrinsic feature of solitons propagating in gain media, and makes the solitons stable in the laser. Furthermore, we show that the soliton energy quantization observed in the lasers is a natural consequence of the gain competition between the multiple solitons. Enlightened by the numerical result we speculate that multisoliton formation and soliton energy quantization observed in other types of soliton fiber lasers could have a similar mechanism.

In this work we show that the atom-photon bound state (APBS) in zero-temperature structured reservoir without an external excitation is always an entangled state of two qubits. The maximal degree of achievable entanglement depends on the atomic frequency detuning from the band edge. APBS can be produced and effectively controlled by the coherent excitation of the reservoir modes with frequencies outside the gap. The proposed scheme can be used for the single-atom optical memory device.

Inspired by an old idea of von Neumann, we seek a pair of commuting operators $X,P$ which are, in a specific sense, “close” to the canonical noncommuting position and momentum operators $x,p$. The construction of such operators is related to the problem of finding complete sets of orthonormal phase-space-localized states, a problem severely constrained by the Balian-Low theorem. Here these constraints are avoided by restricting attention to situations in which the density matrix is reasonably decohered (i.e., spread out in phase space). Commuting position and momentum operators are argued to be of use in discussions of emergent classicality from quantum mechanics. In particular, they may be used to give a discussion of the relationship between exact and approximate decoherence in the decoherent-histories approach to quantum theory.

The Heisenberg uncertainty relation sets a fundamental limit for quantum measurement of incompatible observables. Its standard form derived by Weyl and Robertson is of purely quantum nature when the state is pure. However, for mixed states, because the variance involving a mixed state is a hybrid of classical and quantum uncertainty, the conventional uncertainty relation is of a “mixed” flavor. It is desirable to seek some decomposition of variance into classical and quantum parts and to cast the Heisenberg uncertainty relation for mixed states in a more quantum form. By use of the skew information introduced by Wigner and Yanase in 1963, we make such an attempt and establish a different uncertainty relation which is stronger than the conventional one.

A new class of state transformations that are quantum mechanically prohibited is introduced. These can be seen as the generalization of the universal-NOT transformation which, for all pure inputs state of a given Hilbert space, produces pure outputs whose projection on the original state is fixed to a value smaller than 1. The case of not pure output states is also addressed. We give an application of these transformations in the context of separability criteria.

Quantification of entanglement against mixing is given for a system of coupled qubits under a phase damping channel. A family of pure initial joint states is defined, ranging from pure separable states to maximally entangled states. An ordering of entanglement measures is given for a well-defined initial-state amount of entanglement.

Nonadiabatic alignment of symmetric top molecules induced by a linearly polarized, moderately intense picosecond laser pulse is studied theoretically and experimentally. Our studies are based on the combination of a nonperturbative solution of the Schrödinger equation with femtosecond time-resolved photofragment imaging. Using methyliodide and tert-butyliodide as examples, we calculate and measure the alignment dynamics, focusing on the temporal structure and intensity of the revival patterns, including their dependence on the pulse duration, and their behavior at long times, where centrifugal distortion effects become important. Very good agreement is found between the experimental and numerical results. This allows us to use our theory and numerical results to provide additional insight into the origin of the experimental findings.

We discuss a radio-frequency (rf) ion trap, the rotating-radio-frequency (rotating-rf) trap, in which the motion of a charged particle is described by trigonometric functions rather than the usual Mathieu functions of a normal rf trap. In the rotating-rf trap, a rotating quadrupole electric field confines charged particles, whereas in a normal rf trap, an oscillating quadrupole electric field does. Ion motion in a rotating-rf trap is a superposition of two nondegenerate circular secular motions and two corresponding circular micromotions. The cases of applying a uniform dc magnetic field or a quadrupole dc electric field in addition to the rotating-rf field are also discussed. Confinement in a rotating-rf trap can be tighter than in a normal linear rf trap with the same experimental parameter values.

An optical frequency standard based on the $S\text{−}D$ transition of trapped ${}^{43}\mathrm{Ca}^{+}$ is possible by using just laser diodes for cooling and probing. We discuss two open problems related to the feasibility of this frequency standard, the attainable frequency uncertainty and the method of initial-state preparation. The uncertainty of the clock transition frequency can be so small as $1\times {10}^{-15}$. Using a laser system consisting of three lasers at different detunings and polarizations, the ion can be cooled down to the Lamb-Dicke regime and then prepared in the $m=0$ state within a period much shorter than the cooling period without being heated. The details of our numerical simulation are described.

We present a quantum-mechanical description of parametric down conversion and phase matching of Bloch waves in nonlinear photonic crystals. We discuss the theory in one-dimensional Bragg structures giving a recipe for calculating the down-converted emission strength and direction. We exemplify the discussion by making explicit analytical predictions for the emission amplitude and direction from a one-dimensional structure that consists of alternating layers of ${\mathrm{Al}}_{0.4}{\mathrm{Ga}}_{0.6}\mathrm{As}$ and air. We show that the emission is suitable for the extraction of polarization-entangled photons.

This Brief Report is concerned with the discrete spectrum of the $N$-dimensional Dirac equation. Through the spectral comparison theory demonstrated here the discrete spectrum is obtained approximately without actually having to solve the $N$-dimensional Dirac equation as well as the lower-dimensional cases. This comparison theorem states that if two time-independent attractive potentials are different such that $V_a\prec V_b$, the corresponding energy spectrum satisfies the inequality $E_a\prec E_b$. As an illustrative example, the Hellmann potential is considered with the aid of the comparison theorem and potential envelope method.