We use the bosonization approach to investigate quantum phases of boson-fermion mixtures (BFM) of atoms confined to one dimension by an anisotropic optical lattice. For a BFM with a single species of fermions we find a charge-density wave phase, a fermion pairing phase, and a phase separation regime. We also obtain the rich phase diagram of a BFM with two species of fermions. We demonstrate that these phase diagrams can be understood in terms of polarons, i.e., atoms “dressed” by screening clouds of the other atom species. Techniques to detect the resulting quantum phases are discussed.

We consider insulating states of spin-one bosons in optical lattices in the presence of a weak magnetic field. For the states with more than one atom per lattice site we find a series of quantum phase transitions between states with fixed magnetization and a canted nematic phase. In the presence of a global confining potential, this unusual phase diagram leads to several novel phenomena, including the formation of magnetization plateaus. We discuss how these effects can be observed using spatially resolved spin polarization measurements.

We investigate the Bose-Einstein condensation (BEC, superfluidity) of particle-hole pairs in ultracold fermionic atoms with repulsive interactions and arbitrary polarization, which are trapped within optical lattices. In the strongly repulsive limit, the dynamics of particle-hole pairs can be described by a hard-core Bose-Hubbard model. The insulator-superfluid and charge-density-wave- (CDW) superfluid phase transitions can be induced by decreasing and increasing the potential depths with controlling the trapping laser intensity, respectively. The parameter and polarization dependence of the critical temperatures for the ordered states (BEC and/or CDW) are discussed simultaneously.

We study a square-lattice three-state Potts antiferromagnet with a staggered polarization field at finite temperature. Numerically treating the transfer matrices, we determine two phase boundaries separating the model-parameter space into three parts. We confirm that one of them belongs to the ferromagnetic three-state Potts criticality, which is in accord with a recent prediction, and another to the Ising-type; these are both corresponding to the massless renormalization-group flows stemming from the Gaussian fixed points. We also discuss a field theory to describe the latter Ising transition.

Photon trajectories in incoherent radiation trapping for Doppler, Lorentz, and Voigt line shapes under complete frequency redistribution are shown to be Lévy flights. The jump length ($r$) distributions display characteristic long tails. For the Lorentz line shape, the asymptotic form is a strict power law $r^{-3/2}$, while for Doppler the asymptotic is $r^{-2}(\ln r{)}^{-1/2}$. For the Voigt profile, the asymptotic form always has a Lorentz character, but the trajectory is a self-affine fractal with two characteristic Hausdorff scaling exponents.

We investigate theoretically and experimentally the center-of-mass motion of an ideal Fermi gas in a combined periodic and harmonic potential. We find a crossover from a conducting to an insulating regime as the Fermi energy moves from the first Bloch band into the band gap of the lattice. The conducting regime is characterized by an oscillation of the cloud about the potential minimum, while in the insulating case the center of mass remains on one side of the potential.

We show that fermionic atoms have crucial advantages over bosonic atoms in terms of loading in optical lattices for use as a possible quantum computation device. After analyzing the change in the level structure of a nonuniform confining potential as a periodic potential is superimposed to it, we show how this structure combined with the Pauli principle and fermion degeneracy can be exploited to create unit occupancy of the lattice sites with very high efficiency.

We examine the contribution of pairing fluctuations to the superfluid order parameter for harmonically trapped atomic Fermi gases in the BCS regime. In the limit of small systems we consider, both analytically and numerically, their space and temperature dependence. We predict a parity effect, i.e., that pairing fluctuations show a maximum or a minimum at the center of the trap, depending on the value of the last occupied shell being even or odd. We propose to detect pairing fluctuations by measuring the density-density correlation function after a ballistic expansion of the gas.

We show that soft-core bosons in two dimensions with a ring exchange term exhibit a tendency for phase separation. This observation suggests that the thermodynamic stability of normal Bose liquid phases driven by ring exchange should be carefully examined.

We investigate textbook QED in the framework of the exact renormalization group. In the strong-coupling region, we study the influence of fluctuation-induced photonic and fermionic self-interactions on the nonperturbative running of the gauge coupling. Our findings confirm the triviality hypothesis of complete charge screening if the ultraviolet cutoff is sent to infinity. Though the Landau pole does not belong to the physical coupling domain owing to spontaneous chiral-symmetry-breaking ($\chi$SB), the theory predicts a scale of maximal UV extension of the same order as the Landau pole scale. In addition, we verify that the $\chi \mathrm{S}\mathrm{B}$ phase of the theory which is characterized by a light fermion and a Goldstone boson also has a trivial Yukawa coupling.

Within the classical Maxwell-Chern-Simons limit of the standard-model extension, the emission of light by uniformly moving charges is studied confirming the possibility of a Čerenkov-type effect. In this context, the exact radiation rate for charged magnetic point dipoles is determined and found in agreement with a phase-space estimate under certain assumptions.

This Letter presents the first rigorous proof of the conjecture raised by Gisin and Bechmann-Pasquinucci [Phys. Lett. A 246, 1 (1998)], that the Greenberger-Horne-Zeilinger states of $n$ qubits and the states obtained from them by local unitary transformations are the unique states that maximally violate the Bell-Klyshko inequalities. The proof is obtained by using the certain algebraic properties that Pauli’s matrices satisfy and some subtle mathematical techniques. Since all states obtained by local unitary transformations of a maximally entangled state are equally valid entangled states, we thus give a characterization of maximally entangled states of $n$ qubits in terms of the Bell-type inequality.

We propose a simple quantum network to detect multipartite entangled states of bosons and show how to implement this network for neutral atoms stored in an optical lattice. We investigate the special properties of cluster states, multipartite entangled states, and superpositions of distinct macroscopic quantum states that can be identified by the network.

We experimentally demonstrate the concept of continuous variable quantum erasing. The amplitude quadrature of the signal state is labeled to another state via a quantum nondemolition interaction, leading to a large uncertainty in the determination of the phase quadrature due to the inextricable complementarity of the two observables. We show that by erasing the amplitude quadrature information we are able to recover the phase quadrature information of the signal state.

Theoretical predictions for the Bardeen-Cooper-Schrieffer–Bose-Einstein condensation crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of ${}^{\mathrm{6}}\mathrm{L}\mathrm{i}$. The calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean-field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zero-temperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.

We propose a method to achieve scalable quantum computation based on fast quantum gates on an array of trapped ions, without the requirement of ion shuttling. Conditional quantum gates are obtained for any neighboring ions through spin-dependent acceleration of the ions from periodic photon kicks. The gates are shown to be robust to influence all the other ions in the array and insensitive to the ions' temperature.

Apart from subtle violations of $CP$ symmetry by the weak interactions, the basic laws of physics are time-reversal invariant. Nevertheless, in the macroscopic world, time has a very definite direction, or arrow. Given that the dynamics of a closed system are time-reversal invariant, the arrow of time is introduced through boundary or initial conditions. In this Letter it is argued that if the Hamiltonian for a system, $H$, has the property $\mathcal{T}H{\mathcal{T}}^{-1}=-H$ for a unitary transformation $\mathcal{T}$, then the system can, in principle, be made to evolve backward in time. The prototype of this sort of behavior is the spin echo. Calculations for a single-band tight-binding model suggest that it may be possible to observe the electronic counterpart, or charge echo.

The dynamics of multiple domain formation caused by the modulation instability of two-component Bose-Einstein condensates in an axially symmetric trap are studied by numerically integrating the coupled Gross-Pitaevskii equations. The modulation instability induced by the intercomponent mean-field coupling occurs in the out-of-phase fluctuation of the wave function and leads to the formation of multiple domains that alternate from one domain to another, where the phase of one component jumps across the density dips where the domains of the other exist. This behavior is analogous to a soliton train, which explains the origin of the long lifetime of the spin domains observed by Miesner et al. [Phys. Rev. Lett. 82, 2228 (1999)].

We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.

The limits posed by physics to the quantity of information that can be transmitted with a certain amount of power are investigated. The same ultimate limits are found for transmission of information encoded using matter and massless fields.