Degenerate Fermi gas interacting with molecules near a Feshbach resonance is unstable with respect to the formation of a mixed state, in which atoms and molecules coexist as a coherent superposition. A theory of this state is developed using a mapping to the Dicke model, treating the molecular field in the single mode approximation. The results are accurate in the strong coupling regime relevant for current experimental efforts. The exact solution of the Dicke model is exploited to study stability, phase diagram, and nonadiabatic dynamics of the molecular field in the mixed state.

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a fluctuating force generated by a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate Green’s functions and discuss relaxation and dephasing of a single extra particle added above the Fermi sea. We also extend our analysis to a more generic coupling between system and bath that results in complete thermalization of the system.

A new approach to finite basis sets for the Dirac equation is developed. It does not involve spurious states and improves the convergence properties of basis-set calculations. Efficiency of the method is demonstrated for finite basis sets constructed from $B$ splines by calculating the one-loop self-energy correction for a hydrogenlike ion.

We develop a unified theory of dynamically suppressed decay and decoherence by external fields in qubits coupled to arbitrary thermal baths and dephasing sources. This general theory does not invoke the rotating-wave approximation, which fails for ultrafast field-induced modulations of qubit-bath coupling. Considerations for optimizing the dynamical suppression are outlined.

We propose expanding the space of variations in traditional variational calculations for the energy by considering the wave function $\psi$ to be a functional of a set of functions $\chi :\psi =\psi [\chi ]$, rather than a function. A constrained search in a subspace over all functions $\chi$ such that the functional $\psi [\chi ]$ satisfies a sum rule or leads to a physical observable is then performed. An upper bound to the energy is subsequently obtained by variational minimization. The rigorous construction of such a constrained-search–variational wave function functional is demonstrated.

Rabi nutations of a single nuclear spin in a solid have been observed. The experiments were carried out on a single electron and a single ${}^{13}\mathrm{C}$ nuclear spin of a single nitrogen-vacancy defect center in diamond. The system was used for implementation of quantum logical NOT and a conditional two-qubit gate (CROT). Density matrix tomography of the CROT gate shows that the gate fidelity achieved in our experiments is up to 0.9, good enough to be used in quantum algorithms.

We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on $n$ qubits—a unitary transformation with $4^n$ degrees of freedom. For synthesizing the gate sequence, a method based on the so-called cosine-sine matrix decomposition is presented. The result is optimal in the number of elementary one-qubit gates, $4^n$, and scales more favorably than the previously reported decompositions requiring $4^n-2^{n+1}$ controlled NOT gates.

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters $\alpha$ and $\beta$ can be eliminated. It is found that $\beta$ does not depend on a Renyi parameter $q$ and can be expressed in terms of an exponent $\kappa$ of the power-law Hamiltonian and an average energy $U$. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at $q=1/(1+\kappa )$ that can be considered as the most probable value of $q$ when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such $q$ becomes a power-law distribution with the exponent $-(\kappa +1)$. When $q=1/(1+\kappa )+ϵ$ ($0<ϵ\ll 1$) there appears a horizontal head part of the Renyi distribution that precedes the power-law part. Such a picture corresponds to some observed phenomena.

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length $L(t)\sim t^{1/z}$, we find that for times $t^{\prime }$ and $t$ satisfying $L(t^{\prime })\ll L(t)\ll L(t^{\prime }{)}^{\varphi }$ well inside the scaling regime, the spin autocorrelation function behaves like $\langle s(t)s(t^{\prime })\rangle \sim L(t^{\prime }{)}^{-(d-2+\eta )}[L(t^{\prime })/L(t){]}^{{\lambda }_c^{\prime }}$. For the $O(n)$ model in the $n\to \infty$ limit, we show that ${\lambda }_c^{\prime }=d+2$ and $\varphi =z/2$. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension $d$ and spin vector dimension $n$. We present numerical simulations for the conserved Ising model in $d=1$ and $d=2$, which are fully consistent with the present theory.

We put forward a general procedure to obtain an approximate free-energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.

We study corrections to the Heisenberg interaction between several lateral, single-electron quantum dots. We show, using exact diagonalization, that three-body chiral terms couple triangular configurations to external sources of flux rather strongly. The chiral corrections impact single-qubit encodings utilizing loops of three or more Heisenberg coupled quantum dots.

We study the localization and addressability of ultracold atoms in a combined parabolic and periodic potential. Such a potential supports the existence of localized stationary states and we show that applying a radio frequency field allows us to selectively address atoms in these states. This method is used to measure the energy and momentum distribution of the atoms in the localized states. We also discuss possible extensions of this scheme to address and manipulate atoms in single lattice sites.

The degree of entanglement in an open quantum system varies according to how information in the environment is read. A measure of this contextual entanglement is introduced based on quantum trajectory unravelings of the open system dynamics. It is used to characterize the entanglement in a driven quantum system of dimension $2\times \infty$ where the entanglement is induced by the environmental interaction. A detailed mechanism for the environment-induced entanglement is given.

We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of ${}^{40}\mathrm{K}$ and ${}^6\mathrm{L}\mathrm{i}$ atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau-Zener transition but faster than “the collision rate” in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin states, required to enable $s$-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter, thereby increasing the conversion efficiency; “the collision rate” is the pair decorrelation rate.

We present a model of quantum teleportation protocol based on a double quantum dot array. The unknown qubit is encoded using a pair of quantum dots, with one excess electron, coupled by tunneling. It is shown how to create a maximally entangled state using an adiabatically increasing Coulomb repulsion between different dot pairs. This entangled state is exploited to perform teleportation again using an adiabatic coupling between itself and the incoming unknown state. Finally, a sudden separation of Bob's qubit allows a time evolution of Alice's, which amounts to a modified version of standard Bell measurement. A transmission over a long distance could be obtained by considering the entangled state of a chain of $N$ coupled double quantum dots. The system is shown to be increasingly robust with $N$ against decoherence due to phonons.

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system can have a negative entropy production rate, and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external force, which includes the transverse Lorentz force, leading to equilibrium.

We study specific properties of particles transport by exploring an exact solvable model, a so-called comb structure, where diffusive transport of particles leads to subdiffusion. A performance of the Lévy-like process enriches this transport phenomenon. It is shown that an inhomogeneous convection flow is a mechanism for the realization of the Lévy-like process. It leads to superdiffusion of particles on the comb structure. This superdiffusion is an enhanced one with an arbitrary large transport exponent, but all moments are finite. A frontier case of superdiffusion, where the transport exponent approaches infinity, is studied. The log-normal distribution with the exponentially fast superdiffusion is obtained for this case.

We prove the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse. In contrast with implementations in which a weak pulse is used as a substitute for a single-photon source, the achievable key rate is found to decrease only linearly with the transmission of the channel.

The exact conditions on valid probe states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any probe state with vanishing probability current density. This condition is found both for weak measurements of noncommuting observables and for $c$-number observables. In addition, the interaction between object and probe must be sufficiently weak. Strange weak values can be observed also with mixed probe states, but not for $c$-number observables.

We construct a quantum mechanical perturbation theory which uses the multiple time scale technique. Working with the time translation operator, we use a variant on the method of Bender and Bettencourt. Our perturbation theory smoothly crosses over to the classical result as $\mathrm{\hslash }\mathrm{\to }\mathrm{0}$. It is seen that this technique has a nonperturbative element built into it.