The uncertainty relation between the noise operator and the conserved quantity leads to a bound on the accuracy of general measurements. The bound extends the assertion by Wigner, Araki, and Yanase that conservation laws limit the accuracy of “repeatable,” or “nondisturbing,” measurements to general measurements, and improves the one previously obtained by Yanase for spin measurements. The bound represents an obstacle to making a small quantum computer.

We suggest a system in which the amplitude of macroscopic flux tunneling can be modulated via the Aharonov-Casher effect. The system is an rf SQUID with the Josephson junction replaced by a Bloch transistor—two junctions separated by a small superconducting island on which the charge can be induced by an external gate voltage. When the Josephson coupling energies of the junctions are equal and the induced charge is $q=e$, destructive interference between tunneling paths brings the flux tunneling rate to zero. The device may also be useful as a qubit for quantum computation.

By using a laser and maser in tandem, it is possible to obtain laser action in the hot exhaust gases of a heat engine. Such a “quantum afterburner” involves the internal quantum states of the working molecules as well as the techniques of cavity quantum electrodynamics and is therefore in the domain of quantum thermodynamics. It is shown that Otto cycle engine performance can be improved beyond that of the “ideal” Otto heat engine. Furthermore, the present work demonstrates a new kind of lasing without initial inversion.

We study the nonequilibrium fluctuation-dissipation theorem (FDT) in the glass phase of Bouchaud’s trap model. We incorporate an arbitrary observable $m$ and obtain its correlation and response functions in closed form. A limiting nonequilibrium FDT plot is approached at long times for most choices of $m$. In contrast to standard mean field models, however, the shape of the plot depends nontrivially on the observable, and its slope varies continuously even though there is a single scaling of relaxation times with age. Nonequilibrium FDT plots can therefore not be used to define a meaningful effective temperature $T_{\mathrm{eff}}$ in this model. Consequences for the wider applicability of an FDT-derived $T_{\mathrm{eff}}$ are discussed.

We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensembles—lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance.

We generalize Bell’s inequalities to biparty systems with continuous quantum variables. This is achieved by introducing the Bell operator in perfect analogy to the usual spin- $1/2$ systems. It is then demonstrated that two-mode squeezed vacuum states display quantum nonlocality by using the generalized Bell operator. In particular, the original Einstein-Podolsky-Rosen states, which are the limiting case of the two-mode squeezed vacuum states, can maximally violate Bell’s inequality due to Clauser, Horne, Shimony, and Holt. The experimental aspect of our scheme is briefly considered.

We have experimentally investigated a spin excitation in a quantum degenerate Fermi gas of atoms. In the hydrodynamic regime the damping time of the collective excitation is used to probe the quantum behavior of the gas. At temperatures below the Fermi temperature we measure up to a factor of 2 reduction in the excitation damping time compared to the classical expectation. In addition, we observe a strong excitation energy dependence for this quantum statistical effect.

We develop a novel approach to Bell inequalities based on a constraint that the correlations exhibited by local variable theories must satisfy. This is used to construct a family of Bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise. In particular, our work gives an analytic description of previous numerical results and generalizes them to arbitrarily high dimensionality.

Experimental evidence of stochastic resonance in an excitable optical system is reported. We apply a sinusoidal forcing to the system and, for a finite external noise level, we find a frequency for which the excitable pulsing occurs periodically at the frequency imposed by the modulation. This resonant frequency matches the inverse of the average escape time of the stochastically driven system (i.e., without forcing). The same resonance is found by varying the noise level for fixed forcing frequencies. We discuss different indicators in order to describe quantitatively the degree of resonance.

We derive new Bell’s inequalities for entangled $K^0{\overline{K}}^0$ pairs. This requires (1) mutually exclusive setups allowing either $K^0$ vs ${\overline{K}}^0$ or $K_S$ vs $K_L$ detection and (2) the use of kaon regenerators. The inequalities turn out to be significantly violated by quantum mechanics, resulting in interesting tests of local realism at $\phi$ factories and $p\overline{p}$ machines.

We study a dilute Bose gas of atoms whose scattering length $a$ is large compared to the range of their interaction. We calculate the energy density $E$ of a homogeneous Bose-Einstein condensate (BEC) to second order in the low-density expansion, expressing it in terms of $a$ and a second parameter ${\Lambda }_{*}$ that determines the low-energy observables in the three-body sector. The second-order correction to $E$ has a small imaginary part that reflects the instability due to three-body recombination. In the case of a trapped BEC with large negative $a$, we calculate the coefficient of the three-body mean-field term in $E$ in terms of $a$ and ${\Lambda }_{*}$. It can be very large if there is an Efimov state near threshold.

Viewed as approximations to quantum mechanics, classical evolutions can violate the positive semidefiniteness of the density matrix. The nature of the violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical transition. In particular, the late-time Wigner function can become positive without any corresponding approach to classical dynamics. In the light of these results, we emphasize key issues relevant for experiments studying the quantum-classical transition.

We demonstrate the experimental violation of a spin-1 Bell inequality. The spin-1 inequality is based on the Clauser, Horne, Shimony, and Holt formalism. For entangled spin-1 particles, the maximum quantum-mechanical prediction is 2.55 as opposed to a maximum of 2, predicted using local hidden variables. We obtained an experimental value of $2.27\pm 0.02$ using the four-photon state generated by pulsed, type-II, stimulated parametric down-conversion. This is a violation of the spin-1 Bell inequality by more than 13 standard deviations.

We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving three tiles which sample the tiling sets via Monte Carlo Markov chains. We determine the ergodic times of these dynamical systems (at infinite temperature): they grow with the system size $N_T$ like $\mathrm{const}.\mathrm{}\times N_T^2\ln N_T$; these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets and a powerful tool from probability theory, the coupling technique. We also point out the interesting occurrence of Gumbel distributions.

Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein’s formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. The use of the proposed transformation of variables also shows that fluctuations within Tsallis statistics can be mapped to those of standard statistical mechanics.

We have transported gaseous Bose-Einstein condensates over distances up to 44 cm. This was accomplished by trapping the condensate in the focus of an infrared laser and translating the location of the laser focus with controlled acceleration. Condensates of order ${10}^6$ atoms were moved into an auxiliary chamber and loaded into a magnetic trap formed by a Z-shaped wire. This transport technique avoids the optical and mechanical access constraints of conventional condensate experiments and creates many new scientific opportunities.

We modify the $J$-matrix technique for scattering so that problems with long-range interactions are easily solved. This is done by introducing additional terms in the asymptotic three-term recurrence relation that take into account asymptotic effects of the potential. The solutions of this modified recurrence relation are a very good approximation of the exact scattering solution. Only a small number of residual coefficients need to be calculated. As a result, the numerical effort to solve the scattering problem is seriously reduced. The technique is illustrated with a Yukawa potential.

We have investigated the formation of vortices by rotating the purely magnetic potential confining a Bose-Einstein condensate. We modified the bias field of an axially symmetric TOP trap to create an elliptical potential that rotates in the radial plane. This enabled us to study the conditions for vortex nucleation over a wide range of eccentricities and rotation rates.

We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium is observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.

We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long- and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function describing the state of long-wavelength modes, and thereby to a finite activation rate even at zero temperature. This effect can make a substantial contribution to the total decay rate.