One of the assumptions leading to the Gross-Pitaevskii equation (GPE) is that the interaction between atom pairs can be written effectively as a $\delta$ function so that the interaction range of the particles is assumed to vanish. A simple model that takes into account the extension of the interparticle potential is introduced. The correction to the GPE predictions for the energy of a condensate confined by a harmonic trap in the Thomas-Fermi regime is estimated. Although it is found to be small, we believe that in some situations it can be measured using its dependance on the frequency of the confining trap. Due to the simplicity of the model, it may have a wide range of applications.

Coherent stimulated Raman adiabatic passages (STIRAP) based on a dark state have many applications in diverse quantum systems. In the case of large single-photon detuning in three-level $\Lambda$ systems, one of the bright states almost does not involve the excited state and then acts as the dark state. In this paper, we report the experimental observation of STIRAP based on the dark state, as well as b-STIRAP based on the above bright state, with the same transfer efficiency in a three-level $\Lambda$ cold atomic ensemble. Moreover, both STIRAP and b-STIRAP are found to be immune to the time-varying ac Stark shift. As for a typical example to manipulate a superposition state, we realize an inverse operation on an initial superposition state, which cannot be achieved efficiently for STIRAP based on only the dark state. Our observed double STIRAP thus provides a feasible and robust manner to manipulate quantum states.

We propose a scheme to realize the storage and retrieval of Airy light wave packets in a $\Lambda$-type three-level atomic gas via electromagnetically induced transparency. We first show that (1 + 1)-dimensional Airy light wave packets with very slow propagating velocity and extremely low generation power can be stored and retrieved by switching off and on a control field. We then demonstrate that ultraslow and ultraweak (3 + 1)-dimensional light wave packets, by combining a spatial Bessel or Airy beam with an Airy temporal profile, can also be generated, stored, and retrieved in a controllable way. Because the Airy light wave packets obtained can withstand both diffraction and dispersion in a linear propagation regime, their storage and retrieval are more desirable and promising for quantum information processing in comparison with other types of light wave packets.

The exchange-splitting energy $J$ of the lowest gerade and ungerade states of the ${{\mathrm{H}}_2}^{+}$ molecular ion was calculated using a volume integral expression of symmetry-adapted perturbation theory and standard basis set techniques of quantum chemistry. The performance of the proposed expression was compared to the well-known surface-integral formula. Both formulas involve the primitive function, which we calculated employing either the Hirschfelder-Silbey perturbation theory or the conventional Rayleigh-Schrödinger perturbation theory (the polarization expansion). Our calculations show that very accurate values of $J$ can be obtained using the proposed volume-integral formula. When the Hirschfelder-Silbey primitive function is used in both formulas the volume formula gives much more accurate results than the surface-integral expression. We also show that using the volume-integral formula with the primitive function approximated by Rayleigh-Schrödinger perturbation theory, one correctly obtains only the first four terms in the asymptotic expansion of the exchange-splitting energy.

High-level quantum-chemical calculations are reported for the sulfur electric-field gradients of the CS and SiS molecules. Highly accurate values are obtained in these calculations by using coupled-cluster methods for the treatment of electron correlation together with large atomic-orbital basis sets and by taking into account relativistic effects. The computational results for the sulfur electric-field gradient are used to determine revised values for the ${}^{33}\mathrm{S}$ and ${}^{35}\mathrm{S}$ quadrupole moments, thereby taking advantage of available accurate values for the sulfur quadrupole couplings of CS and SiS from the analysis of rotational spectra. The derived values of $-\mathrm{69.4(4)}$ and 48.3(3) mb for ${}^{33}\mathrm{S}$ and ${}^{35}\mathrm{S}$, respectively, are slightly larger in absolute values than the currently accepted values of $-\mathrm{67.8(13)}$ and 47.1(9) mb and, most importantly, have significantly reduced uncertainties.

We investigate the maximum signal-to-noise ratio per unit time that can be achieved for a spin-1/2 particle subjected to a periodic pulse sequence. Optimal control techniques are applied to design the control field and the position of the steady state, leading to the best signal-to-noise performance. A complete geometric description of the optimal control problem is given in the unbounded case. We show the optimality of the well-known Ernst angle solution, which is widely used in spectroscopic and medical imaging applications, over a large control space allowing the use of shaped pulses.

A quantum emitter coupled to a nanomechanical oscillator is a hybrid system where a macroscopic degree of freedom is coupled to a purely quantum system. Recent progress in nanotechnology has led to the realization of such devices by embedding single artificial atoms, such as quantum dots or superconducting qubits, into vibrating wires or membranes, opening up new perspectives for quantum information technologies and for the exploration of the quantum-classical boundary. In this paper, we show that the quantum emitter can be turned into a strikingly efficient light-controlled source of mechanical power by exploiting constructive interferences of classical phonon fields in the mechanical oscillator. We show that this mechanism can be exploited to carry out low-background nondestructive single-shot measurement of an optically active quantum bit state.

Coherent interconversion between optical and mechanical excitations in an optomechanical cavity can be used to engineer a quantum heat engine. This heat engine is based on an Otto cycle between a cold photonic reservoir and a hot phononic reservoir [K. Zhang, F. Bariani, and P. Meystre, Phys. Rev. Lett. 112, 150602 (2014)]. Building on our previous work, we (i) develop a detailed theoretical analysis of the work and the efficiency of the engine and (ii) perform an investigation of the quantum thermodynamics underlying this scheme. In particular, we analyze the thermodynamic performance in both the dressed polariton picture and the original bare photon and phonon picture. Finally, (iii) a numerical simulation is performed to derive the full evolution of the quantum optomechanical system during the Otto cycle, by taking into account all relevant sources of noise.

The Rabi model considers a two-level system (or spin 1/2) coupled to a quantized harmonic oscillator and describes the simplest interaction between matter and light. The recent experimental progress in solid-state circuit quantum electrodynamics has engendered theoretical efforts to quantitatively describe the mathematical and physical aspects of the light-matter interaction beyond the rotating-wave approximation. We develop a stochastic Schrödinger equation approach which enables us to access the strong-coupling limit of the Rabi model and study the effects of dissipation and ac drive in an exact manner. We include the effect of Ohmic noise on the non-Markovian spin dynamics, resulting in Kondo-type correlations, as well as cavity losses. We compute the time evolution of spin variables in various conditions. As a consideration for future work, we discuss the possibility of reaching a steady state with one polariton in realistic experimental conditions.

We address the microscopic origin of the universal three-body parameter that fixes the spectrum of three-atom systems in the Efimov regime. We identify it with the van der Waals two-body correlation, which causes the three-atom system to deform when the three atoms come within the distance of the van der Waals length, effectively preventing them from coming closer due to the kinetic-energy cost associated with three-body deformation. This deformation mechanism explains the universal ratio of the scattering length at the triatomic resonance to the van der Waals length observed in several experiments and confirmed by numerical calculations.

This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude as the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (in the environment Hamiltonian), memory effects, and symmetry-breaking equilibrium states.

We study transitions of a particle between two wells, separated by a reservoir, under the condition that the particle is not detected in the reservoir. Conventional quantum trajectory theory predicts that such no-result continuous measurement would not affect these transitions. We demonstrate that it holds only for Markovian reservoirs (infinite bandwidth $\Lambda$). In the case of finite $\Lambda$, the probability of the particle's interwell transition is a function of the ratio $\Lambda /\nu$, where $\nu$ is the frequency of measurements. This scaling tells us that in the limit $\nu \to \infty$, the measurement freezes the initial state (the quantum Zeno effect), whereas for $\Lambda \to \infty$ it does not affect the particle's transition across the reservoir. The scaling is proved analytically by deriving a simple formula, which displays two regimes, with the Zeno effect and without the Zeno effect. It also supports a simple explanation of the Zeno effect entirely in terms of the energy-time uncertainty relation, with no explicit use of the projection postulate. Experimental tests of our predictions are discussed.

In this paper we show that the quantum channel between two inertial observers who transmit quantum information by sending realistic photonic wave packets is a well-studied channel in quantum Shannon theory: the Pauli channel. The parameters of the Pauli channel and therefore its classical and quantum capacity depend on the magnitude of the Lorentz boost relating the two observers. The most striking consequence is that two inertial observers whose Pauli channel has initially zero quantum capacity can achieve nonzero quantum communication rates (reaching, in principle, its maximal value, equal to 1) by applying a boost in the right direction. This points to a fundamental connection between quantum channel capacities and special relativity.

The radiation-pressure-induced coupling between an optical cavity field and a mechanical oscillator can create entanglement between them. In previous works this entanglement was treated as that of the quantum fluctuations of the cavity and mechanical modes around their classical mean values. Here we provide a fully quantum approach to optomechanical entanglement, which goes beyond the approximation of classical mean motion plus quantum fluctuation and applies to arbitrary cavity drive. We illustrate the real-time evolution of optomechanical entanglement under drive of arbitrary detuning to show the existence of high, robust, and stable entanglement in the blue-detuned regime and highlight the quantum noise effects that can cause entanglement sudden death and revival.

We show that it is impossible to obtain a quantum speedup for a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous-time oracle model has first been investigated by Shenvi, Brown, and Whaley [Phys. Rev. A 68, 052313 (2003).]. The authors consider a faulty oracle described by a continuous-time master equation that acts as dephasing noise in the basis determined by the marked item. The analysis focuses on the implementation with a particular driving Hamiltonian. A universal lower bound for this oracle model, which rules out a better performance with a different driving Hamiltonian, has so far been lacking. Here, we derive an adversary-type lower bound which shows that the evolution time $T$ has to be at least in the order of $N$, i.e., the size of the search space, when the error rate of the oracle is constant. This means that quadratic quantum speedup vanishes and the runtime assumes again the classical scaling. For the standard quantum oracle model this result was first proven by Regev and Schiff [in Automata, Languages and Programming, Lecture Notes in Computer Science Vol. 5125 (Springer, Berlin, 2008), pp. 773–781]. Here, we extend this result to the continuous-time setting.

We report on the outcomes of a specific study on the quadratic approximation in the partially correlated speed-dependent hard-collision (pC-SDHC) model, which is currently the recommended profile to replace the Voigt convolution for the shape of an isolated line, when perturbed by neutral gas-phase molecules. In particular, we compared the quadratic approximation with the hypergeometric dependence of the collisional relaxation rate on the absorber velocity by using high-quality ${\mathrm{H}}_2{}^{18}\mathrm{O}$ absorption spectra, in coincidence with three vibration-rotation transitions of the ${\nu }_1+{\nu }_3$ band, at 1.39 $\mu$m, also by looking for possible differences in the retrieved parameters. The pC-SDHC profile was found to be quite robust, regardless of the choice of the particular speed dependence. The pressure broadening and shifting parameters, retrieved by using the quadratic and hypergeometric versions, were found to be fully consistent, provided that the velocity-changing collision frequency ${\nu }_{\text{vc}}$ was considered as a free parameter. Similarly, the integrated absorbance was found to be completely unaffected by the choice of the speed dependence, in the entire pressure range we have explored. It must be noted, however, that the velocity-changing collision frequency resulted to be largely overestimated compared to the expected one when using the quadratic approximation. Moreover, the ${\nu }_{\text{vc}}$ values from the quadratic approximation are always significantly larger than those of the hypergeometric model.

For a wide range of magnetic fields, $0\le B\le 2000$ a.u., we present a systematic comparative study of the performance of different types of density-functional approximations in light atoms ($2\le Z\le 6$). Local, generalized-gradient approximation (GGA; semilocal), and meta-GGA ground-state exchange-correlation (xc) functionals are compared on an equal footing with exact-exchange, Hartree-Fock (HF), and current-density-functional-theory (CDFT) approximations. Comparison also is made with published quantum Monte Carlo data. Though all approximations give qualitatively reasonable results, the exchange energies from local and GGA functionals are too negative for large $B$. Results from the Perdew-Burke-Ernzerhof ground-state GGA and Tao-Perdew-Staroverov-Scuseria (TPSS) ground-state meta-GGA functionals are very close. Because of confinement, self-interaction error in such functionals is more severe at large $B$ than at $B=0$, hence self-interaction correction is crucial. Exact exchange combined with the TPSS correlation functional results in a self-interaction-free (xc) functional, from which we obtain atomic energies of comparable accuracy to those from correlated wave-function methods. Specifically for the B and C atoms, we provide beyond-HF energies in a wide range of $B$ fields. Fully self-consistent CDFT calculations were done with the Vignale-Rasolt-Geldart (VRG) functional in conjunction with the PW92 xc functional. Current effects turn out to be small, and the vorticity variable in the VRG functional diverges in some low-density regions. This part of the study suggests that nonlocal, self-interaction-free functionals may be better than local approximations as a starting point for CDFT functional construction and that some basic variable other than the vorticity could be helpful in making CDFT calculations practical.

The theory of pair density is extended to excited states. The theory of a single excited state is generalized for the pair density. A two-particle equation is derived for the square root of the pair density of the given excited state. An expression for the effective potential of this equation is presented.

We study the collisional properties of an ultracold mixture of cesium atoms and dimers close to a Feshbach resonance near 550 G in the regime of positive $s$-wave scattering lengths. We observe an atom-dimer loss resonance that is related to Efimov's scenario of trimer states. The resonance is found at a value of the scattering length that is different from a previous observation at low magnetic fields. This indicates nonuniversal behavior of the Efimov spectrum for positive scattering lengths. We compare our observations with predictions from effective field theory and with a recent model based on the van der Waals interaction. We present additional measurements on pure atomic samples in order to check for the presence of a resonant loss feature related to an avalanche effect, as suggested by observations in other atomic species. We could not confirm the presence of such a feature.

So far, the interaction of ultracold atoms can only be tuned within one particular scattering channel near a resonance, where the spinor structure of atomic isotopes is destroyed due to the typically large magnetic field. In this work, we propose a scheme to realize multichannel scattering resonance (MCSR) of ultracold bosons in one-dimension while still keeping their spinor structure. The MCSR refers to a simultaneous scattering resonance among all different scattering channels, including those breaking SU(2) and SO(2) spin-rotation symmetries. Essential ingredients for MCSR include the three-dimensional interactions, the confinement potential, and a spin-flipping field. Near MCSR a many-body spinor system exhibits exotic spin-density distributions and pair correlations, which are significantly different from those near a single-channel resonance.