The recent experimental realization of spin-orbit coupling for ultracold atoms has generated much interest in the physics of spin-orbit-coupled degenerate Fermi gases. Although recently the BCS-BEC crossover in three-dimensional (3D) spin-orbit-coupled Fermi gases has been intensively studied, the corresponding two-dimensional (2D) crossover physics has remained unexplored. In this paper, we investigate, both numerically and analytically, the BCS-BEC crossover physics in 2D degenerate Fermi gases in the presence of the Rashba type of spin-orbit coupling. We derive the mean-field gap and atom-number equations suitable for 2D spin-orbit-coupled Fermi gases and solve them numerically and self-consistently, from which the dependence of the ground-state properties (chemical potential, superfluid pairing gap, ground-state energy per atom) on the system parameters (e.g., binding energy, spin-orbit-coupling strength) is obtained. Furthermore, we derive analytical expressions for these ground-state quantities, which agree well with our numerical results within a broad parameter region. Such analytical expressions also agree qualitatively with previous numerical results for 3D spin-orbit-coupled Fermi gases, where analytical results are lacking. We show that, with increasing spin-orbit coupling (SOC) strength, the chemical potential is shifted by a constant determined by the SOC strength. The superfluid pairing gap is enhanced significantly in the BCS limit for strong SOC, but increases only slightly in the BEC limit.

The interfacial instability and subsequent dynamics in a phase-separated two-component Bose-Einstein condensate with rotational symmetry are studied. When the interatomic interaction or the trap frequency is changed, the Rayleigh-Taylor instability breaks the rotational symmetry of the interface, which is subsequently deformed into nonlinear patterns including mushroom shapes.

We investigate the quantum and thermal phase diagram of fermionic polar molecules loaded in a bilayer trapping potential with perpendicular dipole moment. We use both a BCS-theory approach that is most reliable at weak coupling and a strong-coupling approach that considers the two-body bound dimer states with one molecule in each layer as the relevant degree of freedom. The system ground state is a Bose-Einstein condensate (BEC) of dimer bound states in the low-density limit and a paired superfluid (BCS) state in the high-density limit. At zero temperature, the intralayer repulsion is found to broaden the regime of BCS-BEC crossover and can potentially induce system collapse through the softening of roton excitations. The BCS theory and the strongly coupled dimer picture yield similar predictions for the parameters of the crossover regime. The Berezinskii-Kosterlitz-Thouless transition temperature of the dimer superfluid is also calculated. The crossover can be driven by many-body effects and is strongly affected by the intralayer interaction which was ignored in previous studies.

We explore bright soliton solutions of ultracold Bose-Fermi gases, showing that the presence of $p$-wave interactions can remove the usual collapse instability and support stable soliton solutions that are global energy minima. A variational model that incorporates the relevant $s$- and $p$-wave interactions in the system is established analytically and solved to probe the dependencies of the soliton stationary states on key experimental parameters. Under attractive $s$-wave interactions, bright solitons exist only as metastable states susceptible to collapse. Remarkably, the presence of repulsive $p$-wave interactions alleviates this collapse instability. This dramatically widens the range of experimentally achievable soliton solutions and indicates greatly enhanced robustness. While we focus specifically on the boson-fermion pairing of ${}^{87}$Rb and ${}^{40}$K, the stabilization inferred by repulsive $p$-wave interactions should apply to the wider remit of ultracold Bose-Fermi mixtures.

The theory of nanoparticle sensing using whispering-gallery-mode resonators is investigated for both plasmonic and Rayleigh scatterers. In particular, we describe how to extract critical information, such as the number of particles adsorbed, from the transmission spectrum. The effects of the interference due to multiple interparticle scatterings are elucidated. Analytical expressions are derived so as to enable further numerical analysis.

On the basis of numerical simulation, it is found that powerful long-distance soliton wings can be formed by dispersive waves which are emitted by solitons because of lumped elements in a laser cavity. We analyze peculiarities of the interaction of two solitons through such wings in lasers with lumped saturable absorbers. Various sets of bound steady states of a two-soliton molecule are demonstrated. The relation between the spectral sidebands and the dispersive-wave wings of a soliton is found. The periodic changes in a soliton's profile during its pass through the laser cavity are studied.

Deterministic light-induced spin squeezing in an atomic gas is limited by photon shot noise or, equivalently, by atomic state information escaping with the light field mediating the effective atom-atom interaction. We show theoretically that the performance of cavity spin squeezing [M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, Phys. Rev. A 81, 021804(R) (2010)] can be substantially improved by erasing the light-atom entanglement, and propose several methods for doing so. Accounting for light scattering into free space, quantum erasure improves the scaling of cavity squeezing from $S^{-1/2}$ to $S^{-2/3}$, where $S$ is the total atomic spin.

The Demkov model fails to explain the formation of negative ions in grazing scattering of atoms from insulator surfaces at relatively high velocities, since the electron detachment process is not included in the model. In this work, the well-known quantum tunneling effect for electrons through the repulsive Coulomb barrier has been proposed to describe electron detachment from the formed negative ions. The combination of these two models results in excellent agreement with the experimental data in the overall impact velocity range.

A recent paper [L. Heaney, A. Cabello, M. F. Santos, and V. Vedral, New J. Phys. 13, 053054 (2011)] revealed that a single quantum symmetrically delocalized over $N$ modes, namely a $W$ state, effectively allows for all-versus-nothing proofs of nonlocality in the limit of large $N$. Ideally, this finding opens up the possibility of using the robustness of the $W$ states while realizing the nonlocal behavior previously thought to be exclusive to the more complex class of Greenberger-Horne-Zeilinger states. We show that in practice, however, the slightest decoherence or inefficiency of the Bell measurements on $W$ states will degrade any violation margin gained by scaling to higher $N$. The nonstatistical demonstration of nonlocality is thus proved to be impossible in any realistic experiment.

The propagation of an off-resonant, single-photon pulse in and into a medium of two-level atoms is considered. When the pulse is launched from within the medium, there are two propagation speeds, neither of which is the normal group velocity. For densities as small as 10${}^{11}$ atoms/cm${}^3$ and detunings of order 10${}^{11}$ s${}^{-1}$, both propagation speeds approach one half the speed of light in vacuum. Moreover, rather remarkably, there are Rabi oscillations between the field and atomic excitation, even for this single-photon pulse. In contrast, for a pulse sent into the medium, the atom-field system remains adiabatically in a dressed state that propagates with the normal group velocity. In the limit that the index of refraction is approximately equal to unity, we obtain the Fresnel equations for the reflection and transmission coefficients based on this microscopic model. The transmission coefficient differs from the conventional result owing to the fact that we quantize the field in free space.

A process of preparation, transmission, and subsequent projective measurement of a qubit can be simulated by a classical model with only two bits of communication and some amount of shared randomness. However, to the best of our knowledge, no model for $n$ qubits with a finite amount of classical communication is known at present. A lower bound for the communication cost can provide useful hints for a generalization. It is known, for example, that the amount of communication must be greater than $c{2}^n$, where $c\simeq 0.01$. The proof uses a quite elaborate theorem of communication complexity. Using a mathematical conjecture known as the “double cap conjecture,” we strengthen this result by presenting a geometrical and extremely simple derivation of the lower bound $2^n-1$. Only rank-1 projective measurements are involved in the derivation.

Nonlocalities of Foldy-Wouthuysen and related transformations, which are used to separate positive- and negative-energy states in the Dirac equation, are investigated. Second moments of functional kernels generated by the transformations are calculated, and the transformed functions and their variances are computed. It is shown that all the transformed quantities are smeared in the coordinate space by an amount comparable to the Compton wavelength ${\lambda }_c=\hslash /mc$.

We propose an iterative algorithm for incomplete quantum process tomography with the help of quantum state estimation. The algorithm, which is based on the combined principles of maximum likelihood and maximum entropy, yields a unique estimator for an unknown quantum process when one has less than a complete set of linearly independent measurement data to specify the quantum process uniquely. We apply this iterative algorithm adaptively in various situations and so optimize the amount of resources required to estimate a quantum process with incomplete data.

We consider a one-dimensional loop of circumference $L$ crossed by a constant magnetic flux $\Phi$ and connected to an infinite lead with coupling parameter $\varepsilon$. Assuming that the initial state ${\psi }_0$ of the particle is confined inside the loop and evolves freely, we analyze the time evolution of the nonescape probability $P({\psi }_0,L,\Phi ,\varepsilon ,t)$, which is the probability that the particle will still be inside the loop at some later time $t$. In appropriate units, we found that $P({\psi }_0,L,\Phi ,\varepsilon ,t)=P_{\infty }({\psi }_0,\Phi )+{\sum }_{k=1}^{\infty }{C}_k({\psi }_0,L,\Phi ,\varepsilon )/t^k$. The constant $P_{\infty }({\psi }_0,\Phi )$ is independent of $L$ and $\varepsilon$, and vanishes if ${\psi }_0$ has no bound state components or if $\left|\cos \right(\Phi \left)\right|\ne 1$. The coefficients $C_1({\psi }_0,L,\Phi ,\varepsilon )$ and $C_3({\psi }_0,L,\Phi ,\varepsilon )$ depend on the initial state ${\psi }_0$ of the particle, but only the momentum $k=\Phi /L$ is involved. There are initial states ${\psi }_0$ for which $P({\psi }_0,L,\Phi ,\varepsilon ,t)\sim C_{\delta }({\psi }_0,L,\Phi ,\varepsilon )/t^{\delta }$, as $t\to \infty$, where $\delta =1$ if $\cos \left(\Phi \right)=1$ and $\delta =3$ if $\cos \left(\Phi \right)\ne 1$. Thus, by submitting the loop to an external magnetic flux, one may induce a radical change in the asymptotic decay rate of $P({\psi }_0,L,\Phi ,\varepsilon ,t)$. Interestingly, if $\cos \left(\Phi \right)=1$, then $C_1({\psi }_0,L,\Phi ,\varepsilon )$ decreases with $\varepsilon$ (i.e., the particle escapes faster in the long run) while in the case $\cos \left(\Phi \right)\ne 1$, the coefficient $C_3({\psi }_0,L,\Phi ,\varepsilon )$ increases with $\varepsilon$ (i.e., the particle escapes slower in the long run). Assuming the particle to be initially in a bound state of the loop with $\Phi =0$, we compute explicit relations and present some numerical results showing a global picture in time of $P({\psi }_0,L,\Phi ,\varepsilon ,t)$. Finally, by using the pseudospectral method, we consider the interacting case with soft-core Coulomb potentials.

Many arbitrated quantum signature schemes implemented with the help of a trusted third party have been developed up to now. In order to guarantee unconditional security, most of them take advantage of the optimal quantum one-time encryption based on Pauli operators. However, in this paper we point out that the previous schemes provide security only against a total break attack and show in fact that there exists an existential forgery attack that can validly modify the transmitted pair of message and signature. In addition, we also provide a simple method to recover security against the proposed attack.

We present a fair and optimistic quantum-contract-signing protocol between two clients that requires no communication with the third trusted party during the exchange phase. We discuss its fairness and show that it is possible to design such a protocol for which the probability of a dishonest client to cheat becomes negligible and scales as $N^{-1/2}$, where $N$ is the number of messages exchanged between the clients. Our protocol is not based on the exchange of signed messages: Its fairness is based on the laws of quantum mechanics. Thus, it is abuse free, and the clients do not have to generate new keys for each message during the exchange phase. We discuss a real-life scenario when measurement errors and qubit-state corruption due to noisy channels and imperfect quantum memories occur and argue that for a real, good-enough measurement apparatus, transmission channels, and quantum memories, our protocol would still be fair. Apart from stable quantum memories, the other segments of our protocol could be implemented by today's technology, as they require in essence the same type of apparatus as the one needed for the Bennett-Brassard 1984 (BB84) cryptographic protocol. Finally, we briefly discuss two alternative versions of the protocol, one that uses only two states [based on the Bennett 1992 (B92) protocol] and the other that uses entangled pairs, and show that it is possible to generalize our protocol to an arbitrary number of clients.

We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.