We investigate the response of superfluid Fermi gases to rapid changes of the three-dimensional $s$-wave scattering length $a$ by solving the time-dependent Bogoliubov–de Gennes equations. In general the magnitude of the order parameter $\left|\Delta \right|$ performs oscillations, which are sometimes called the “Higgs” mode, with the angular frequency $2{\Delta }_{\text{gap}}/\hslash$, where ${\Delta }_{\text{gap}}$ is the gap in the spectrum of fermionic excitations. First, we excite the oscillations with a linear ramp of $1/a$ and study the evolution of $\left|\Delta \right|$. Second, we continously drive the system with a sinusoidal modulation of $1/a$. In the first case, the oscillations in $\left|\Delta \right|$ damp according to a power law. In the second case, the continued driving causes revivals in the oscillations. In both cases, the excitation of the oscillations causes a reduction in the time-averaged value of $\left|\Delta \right|$. We propose two experimental protocols, based around the two approaches, to measure the frequency and damping of the oscillations, and hence ${\Delta }_{\text{gap}}$.

We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime can be realized using ultracold Fermi gas coupled to a single-mode cavity. By the functional integral formalism, we derive an effective atom-only action, which mimics the two-component Fermi gas with tunable two-body interaction. First, we address the features of the cavity-mediated interaction. We find that the matter-light coupling creates an effective $s$-wave scattering whose sign and amplitude are controlled by parameters of the cavity. Second, we discuss the fermionic superfluidity on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, and dissociation temperature. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and external pumping field on the pairing correlation are also studied.

We show that parity-time- ($\mathcal{PT}$-) symmetric coupled optical waveguides with gain and loss support localized oscillatory structures similar to the breathers of the classical ${\varphi }^4$ model. The power carried by the $\mathcal{P}\mathcal{T}$ breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and to be prevalent in the products of the soliton collisions. We demonstrate that the evolution of a small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schrödinger equations and employ this Hamiltonian system to show that small-amplitude $\mathcal{P}\mathcal{T}$ breathers are stable.

We describe an equilibrium state of a rotating trapped atomic condensate, which is characterized by a nonzero internal circulation and spontaneous breaking of the rotational O(2) symmetry with all three major semiaxes of the condensate having different values. The macroscopic rotation of the condensate is supported by a mesh of quantized vortices, whose number density is a function of internal circulation. The oscillation modes of this state are computed and the Goldstone mode associated with the loss of the symmetry is identified. The possible avenues for experimental identification of this state are discussed.

Matchgates are a group of two-qubit gates associated with free fermions. They are classically simulatable if restricted to act between nearest neighbors on a one-dimensional chain, but become universal for quantum computation with longer-range interactions. We describe various alternative geometries with nearest-neighbor interactions that result in universal quantum computation with matchgates only, including subtle departures from the chain. Our results pave the way for new quantum computer architectures that rely solely on the simple interactions associated with matchgates.

We present a mathematical proof of the algorithm allowing one to generate all—symmetric and nonsymmetric—total angular momentum eigenstates in remote matter qubits by projective measurements, proposed in Maser et al. [Phys. Rev. A 79, 033833 (2009)]. By deriving a recursion formula for the algorithm we show that the generated states are equal to the total angular momentum eigenstates obtained via the usual quantum-mechanical coupling of angular momenta. In this way we demonstrate that the algorithm is able to simulate the coupling of $N$ spin-1/2 systems, and to implement the required Clebsch-Gordan coefficients, even though the particles never directly interact with each other.

We give details of a simple argument for a security bound for a recently published secure relativistic quantum bit commitment protocol [Phys. Rev. Lett. 109, 130501 (2012)].

This work investigates the use of dynamical decoupling to shield quantum discord from errors introduced by the environment. Specifically, a two-qubit system interacting with independent baths of bosons is considered. The initial conditions of the system were chosen as pure and mixed states, while the dynamical decouplingwas achieved by means of continuous fields. The effect of the temperature on the shielding of quantum discord is also studied. It is shown that although the quantum discord for particular initial states may be perfectly preserved over some finite time window in the absence of any protective field, the effectiveness of the dynamical decoupling with continuous fields depends essentially on the time scale required to preserve quantum discord. It is also shown that for these particular initial states the time for which the shielding of the quantum discord becomes effective decreases as the temperature increases.

We study several extensions of the single-photon, cavity-mediated quantum logical gates recently proposed by Koshino, Ishizaka, and Nakamura [Phys. Rev. A 82, 010301(R) (2010)]: to a double-sided cavity configuration, to the case where the two atomic ground states are nondegenerate, and to the nonadiabatic regime. Our analysis can be used to estimate the effects of various imperfections and to prepare the way for a proof-of-principle demonstration with present technology. We are able to present a full solution for the outgoing pulses, in the frequency domain, which is valid for arbitrary incident pulses and cavity parameters. From this we find, among other results, that the leading correction to the adiabatic approximation can be made to vanish for a suitable choice of detunings, provided the cavity is “good enough” (high enough ratio of coupling to loss). This could significantly relax the need for long single-photon pulses in this scheme.

The Lifshitz formula is derived by making use of the spectral summation method, which is a mathematically rigorous simultaneous application of both the mode-by-mode summation technique and scattering formalism. The contributions to the Casimir energy of electromagnetic excitations of different types (surface modes, waveguide modes, and photonic modes) are clearly retraced. A correct transition to imaginary frequencies is accomplished with allowance for all the peculiarities of the frequency equations and pertinent scattering data in the complex $\omega$ plane, including, in particular, the cuts connecting the branch points and complex roots of the frequency equations (quasinormal modes). The important feature of our approach is a special choice of appropriate passes in the contour integrals which are used for transition to imaginary frequencies. As a result, the longstanding problem of cuts in the complex $\omega$ plane is solved completely. Some subtleties and vague points in previous derivations of the Lifshitz formula are elucidated. For completeness of the presentation, the necessary mathematical facts are also stated, namely, solution of the Maxwell equations for configurations under consideration, scattering formalism for parallel-plane interfaces, determination of the frequency equation roots, and others.

We extract the leading effective-range corrections to the equation of state of the unitary Fermi gas from ab initio fixed-node quantum Monte Carlo (QMC) calculations in a periodic box using a density functional theory (DFT), and show them to be universal by considering several two-body interactions. Furthermore, we find that the DFT is consistent with the best available unbiased QMC calculations, analytic results, and experimental measurements of the equation of state. We also discuss the asymptotic effective-range corrections for trapped systems and present QMC results with the correct asymptotic scaling.

The long-standing debate whether the phase transition in the Dicke model can be realized with dipoles in electromagnetic fields is still an unsettled one. The well-known statement often referred to as the “no-go theorem” asserts that the so-called $A^2$ term, missing from the Dicke model, is relevant and prevents the system from undergoing a phase transition. At variance with this common belief, in this paper we prove that the Dicke model does give a proper description of the interaction of light field with the internal excitation of atoms. The phase transition and the spontaneous formation of a transverse-electric mean field cannot be excluded by principle. We point out that the proper treatment of the single-mode approximation is crucial, wherefore we present a systematic derivation of the dipole gauge inside a perfect Fabry-Pérot cavity from first principles. Besides the impact on the debate around the Dicke phase transition, such a cleanup of the theoretical ground of cavity QED is important because currently there are many emerging experimental approaches to reach strong or even ultrastrong coupling between dipoles and photons, which demand a correct treatment of the Dicke model parameters.

We have studied experimentally the emission of $\gamma$-ray photons by synchrotron-radiation-excited ${}^{57}$Fe nuclei in an iron borate crystal. The crystal was set in the vicinity of the Bragg angle for pure nuclear diffraction of the synchrotron radiation. The electronically forbidden but nuclear-allowed (333) reflection was employed to extract the nuclear scattering signal. The isolation of nuclear scattering was possible for two reasons. First, in contrast to the case of Rayleigh scattering, the phase in nuclear resonant scattering depends on the direction of the magnetic moment. Second, the iron atom spins in a ${}^{57}$FeBO${}_3$ crystal are antiferromagnetically ordered. Because they are flashlike excited by synchrotron radiation, the nuclei in the crystal afterwards emit their own recoil-free radiation within a narrow angular range. The angular dependence of the emission was measured with a highly collimated beam by setting the crystal in different angular positions near the Bragg angle. At room temperature the angular dependence of the emission intensity has a functional form with a single symmetric maximum. However, on approaching the Néel temperature, the angular dependence of the emission intensity is transformed dramatically in shape and width. The maximum broadens greatly, splits, and acquires a double-peak shape. The energy and time distributions of the emitted radiation appear to be strongly dependent on the angular position of the crystal relative to the incident beam within the angular range of the emission. The experimental measurements are fully consistent with theoretical predictions. The results obtained can be used in developing synchrotron-radiation-based techniques with neV resolution.

One of the biggest challenges for implementing quantum devices is the requirement to perform accurate quantum gates. The destructive effects of interactions with the environment present some of the most difficult obstacles that must be overcome for precise quantum control. In this work we implement a proof of principle experiment of quantum gates protected against a fluctuating environment and control pulse errors using dynamical decoupling techniques. We show that decoherence can be reduced during the application of quantum gates. High-fidelity quantum gates can be achieved even if the gate time exceeds the free evolution decoherence time by one order of magnitude and for protected operations consisting of up to 330 individual control pulses.

We present quantum mechanical explanations for unresolved phenomena observed in field-free molecular alignment by a femtosecond laser pulse. Quantum phase analysis of molecular rotational states reveals the physical origin of the following phenomena: strong alignment peaks appear periodically, and the temporal shape of each alignment peak changes in an orderly fashion depending on molecular species; the strongest alignment is not achieved at the first peak; the transition between aligned and antialigned states is very fast compared to the time scale of rotational dynamics. These features are understood in a unified way analogous to that describing a carrier-envelope-phase-stabilized mode-locked laser.

In this paper, we present a coherent feedback control scheme for non-Markovian bosonic systems, in which an engineered quantum control field is introduced to couple both the system and the noise bath. The closed-loop dynamics of the system is described by an exact non-Markovian quantum Langevin equation, where the spectral density functions of the noise and the quantum control field, as well as their coupling, are combined into a single memory kernel function. We show that the coupling between the quantum control field with the noise bath can be used as a feedback control to modulate the memory kernel function. As a result, the noise bath can be driven out of resonance with the system and the decoherence can be efficiently suppressed. The effectiveness of the controllability is demonstrated with a photonic circuit in photonic crystals.

Measurement-device-independent quantum key distribution with a finite number of decoy states is analyzed under finite-data-size assumption. By accounting for statistical fluctuations in parameter estimation, we investigate vacuum+weak- and vacuum+two-weak-decoy-state protocols. In each case, we find proper operation regimes, where the performance of our system is comparable to the asymptotic case for which the key size and the number of decoy states approach infinity. Our results show that practical implementations of this scheme can be both secure and efficient.

We propose a simple feedback-control scheme for adiabatic quantum computation with superconducting flux qubits. The proposed method makes use of existing on-chip hardware to monitor the ground-state curvature, which is then used to control the computation speed to maximize the success probability. We show that this scheme can provide a polynomial speed-up in performance and that it is possible to choose a suitable set of feedback-control parameters for an arbitrary problem Hamiltonian.

The recoil, vacuum polarization, and electron vertex corrections of first and second orders in the fine structure constant $\alpha$ and the ratio of electron to muon and electron to $\alpha$-particle masses are calculated for the hyperfine splitting of the $1s_{1/2}^{\left(e\right)}2s_{1/2}^{\left(\mu \right)}$ state of muonic helium atom $\left(\mu e_2^4\text{He}\right)$ on the basis of perturbation theory. We obtain a total result for the muonically excited state hyperfine splitting $\Delta {\nu }^{\text{hfs}}=4295.66$ MHz, which improves previous calculations, taking additional corrections into account, and a more accurate treatment of the electron vertex contribution.

In this paper, we report relativistic quantum mechanical calculations of widths and shifts of spectral lines in He II ions produced by electron impact. We use the Dirac $R$-matrix method to treat ($N+1$)-electron collision systems to obtain scattering matrices. The present calculations ensure that the atomic structure and collisional data on adequate accuracy are used in our electron-impact broadening technique. A detailed comparison of our results with available experimental and theoretical results shows that our results are typically closer to the experimental ones even for the H$\alpha$ line.