We investigate the single-particle and collective excitations of a Rashba spin-orbit-coupled atomic Fermi gas with attractive interaction, loaded in a two-dimensional (2D) square optical lattice, in the presence of an effective out-of-plane Zeeman field. Our numerical calculations show that the many-body physics of the Bardeen-Cooper-Schrieffer (BCS) side is strongly modified compared to the Fermi gases in the free space. The physics behind this statement lies in the fact that in the 2D lattice case the single-particle ground-state energy is four times degenerated, while without a lattice structure the ground state is infinitely degenerate, and because of that, the spin-orbit coupling (SOC) in optical lattices gives rise to unusual properties entirely different from the continuum. For example, in the continuum, the pairing gap as well as the condensate fraction is strongly enhanced by the SOC strength on the BCS side. In the presence of lattice geometry the gap and the condensate fraction increase as a function of the SOC strength only at small fillings and a weak attraction limit. Moreover, we found that the speed of sound also exhibits different behavior: in the 3D and 2D continua, the slope of the Goldstone mode decreases as a function of the SOC strength, while in the lattice case the speed of sound increases monotonically with the SOC strength.

The complexity of arbitrary dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit—in the form of a limit cycle, dividing surface, instanton trajectories, or some other related structure—can be uncovered. Determining such a periodic orbit, no matter how beguilingly simple it appears, is often very challenging. We present a method for the direct construction of unstable periodic orbits and instanton trajectories at saddle points by means of Lagrangian descriptors. Such structures result from the minimization of a scalar-valued phase-space function without the need for any additional constraints or knowledge. We illustrate the approach for two-degree of freedom systems at a rank-1 saddle point of the underlying potential-energy surface by constructing both periodic orbits at energies above the saddle point as well as instanton trajectories below the saddle-point energy.

The Leggett-Garg inequality holds for any macrorealistic system that is being measured noninvasively. A violation of the inequality can signal that a system does not conform to our primal intuition about the physical world. Alternatively, a violation can simply indicate that a “clumsy” experimental technique led to invasive measurements. Here, we consider a recent Leggett-Garg test designed to try to rule out the mundane second possibility. We tailor this Leggett-Garg test to the IBM 5Q Quantum Experience system and find compelling evidence that qubit $Q_2$ of the system cannot be described by noninvasive macrorealism.

There exist two formulations for quantum heat engines that model energy transfer between two microscopic systems. One is the semiclassical scenario and the other is the full quantum scenario. The former is formulated as unitary evolution for the internal system and is adopted by the statistical mechanics community. In the latter, the whole process is formulated as unitary and is adopted by the quantum information community. This paper proposes a model for quantum heat engines that transfer energy from a collection of microscopic systems to a macroscopic system like a fuel cell. In such a situation, the amount of extracted work is visible for a human. For this purpose, we formulate a quantum heat engine as the measurement process whose measurement outcome is the amount of extracted work. Under this model, we derive a suitable energy-conservation law and propose a more concrete submodel. Then we derive a trade-off relation between the measurability of the amount of work extraction and the coherence of the internal system, which limits the applicability of the semiclassical scenario to a heat engine transferring energy from a collection of microscopic systems to a macroscopic system.

In quantum theory we refer to the probability of finding a particle between positions $x$ and $x+dx$ at the instant $t$, although we have no capacity of predicting exactly when the detection occurs. In this work, we first present an extended nonrelativistic quantum formalism where space and time play equivalent roles. It leads to the probability of finding a particle between $x$ and $x+dx$ during [$t,t+dt$]. Then, we find a Schrödinger-like equation for a “mirror” wave function $\varphi (t,x)$ associated with the probability of measuring the system between $t$ and $t+dt$, given that detection occurs at $x$. In this framework, it is shown that energy measurements of a stationary state display a nonzero dispersion, and that energy-time uncertainty arises from first principles. We show that a central result on arrival time, obtained through approaches that resort to ad hoc assumptions, is a natural, built-in part of the formalism presented here.

We investigate how ultracold atoms in double-well potentials can be used to study and put bounds on models describing wave-function collapse. We refer in particular to the continuous spontaneous localization (CSL) model, which is the most well studied among dynamical reduction models. It modifies the Schrödinger equation in order to include the collapse of the wave function in its dynamics. We consider Bose Josephson junctions, where ultracold bosons are trapped in a double-well potential, since they can be experimentally controlled with high accuracy and are suited and used to study macroscopic quantum phenomena on a scale of microns, with a number of particles typically ranging from $\sim {10}^2–{10}^3$ to $\sim {10}^5–{10}^6$. We study the CSL dynamics of three atomic states showing macroscopic quantum coherence: the atomic coherent state, the superposition of two atomic coherent states, and the NOON state. We show that for the last two states, the suppression of quantum coherence induced by the CSL model increases exponentially with the number of atoms. We observe that in the case of optically trapped atoms, the spontaneous photon emission of the atoms induces a dynamics similar to the CSL one, and we conclude that magnetically trapped atoms may be more convenient to experimentally test the CSL model. Finally, we discuss decoherence effects in order to provide reasonable estimates on the bounds that it is (or will be) possible to obtain for the parameters of the CSL model in such class of experiments. As an example, we show that a NOON state with $N\sim {10}^3$ with a coherence time of $\sim 1$ s can constrain the CSL parameters in a region where the other systems presently cannot.

Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the auxiliary fermion transformation. The Bravyi-Kitaev transform is reformulated in terms of a classical data structure and generalized to achieve a further locality improvement for local fermionic models on a rectangular lattice. We conclude that the most compact encoding of the fermionic operators can be done using ancilla qubits with the auxiliary fermion scheme. Without introducing ancillas, a variant of the Bravyi-Kitaev transform provides the most compact fermion-to-qubit mapping for Hubbard-like models.

A set of simple analytic formulas is derived via electrostatics-based methods to accurately calculate the values of electron affinities $A_n$ and ionization potentials $I_n$ for $n$-carbon icosahedral fullerene molecules as a function of their average radii $R_n$. These formulas reproduce with accuracy the values of $A_n, I_n$, and their scalings with $1/R_n$ that were determined previously in detailed, computationally intensive density functional theory calculations. The formula for $A_n$ is derived from an enhanced image-charge model that treats the valence region of the icosahedral system as a quasispherical conductor of radius $(R_n+\delta )$, where $\delta =1/4W_{\infty }$ is a small constant distance determined from the work function $W_{\infty }$ of graphene. Using this model, though, a formula for $I_n$ that includes only electrostatics-like terms does not exhibit accuracy similar to the analogous formula for $A_n$. To make it accurate, a term must be added to account for the large symmetry-induced quantum energy gap in the valence energy levels (i.e., the HOMO-LUMO gap). An elementary two-state model based upon a quantum rotor succeeds in producing a simple expression that evaluates the energy gap as an explicit function of $A_n$. Adding this to the electrostatics-like formula for $I_n$ gives a simple quantum equation that yields accurate values for $I_n$ and expresses them as a function of $A_n$. Further, the simple equations for $A_n$ and $I_n$ yield significant insight into both the physics of electron detachment in the fullerenes and the scaling with $R_n$ of their quantum capacitances $C_n=1/(I_n-A_n)$.

This paper investigates the Fano-Feshbach resonance with a two-channel coupled-square-well model in both the frequency and time domains. This system is shown to exhibit Fano line-shape profiles in the energy absorption spectrum. The associated time-dependent transition moment response has a phase shift that has recently been understood to be related to the Fano line-shape asymmetric $q$ parameter by $\phi =2arg(q-i)$. The present study demonstrates that the phase-$q$ correspondence is general for any Fano resonance in the weak-coupling regime, independent of the transition mechanism.

A universal interference structure is found in the photoelectron momentum distribution of atoms in intense infrared laser field. Theoretical analysis shows that this structure can be attributed to a form of Coulomb-field-driven backward-scattering photoelectrons in the direction perpendicular to the laser field, in contrast to the conventional rescattering along the laser polarization direction. This transverse backward-scattering process is closely related to a family of photoelectrons initially ionized within a time interval of less than 200 as around the crest of the laser electric field. Those electrons, acquiring near-zero return energy in the laser field, will be pulled back solely by the ionic Coulomb field and backscattered in the transverse direction. Moreover, this rescattering process mainly occurs at the first or second return time, giving rise to different phases of the photoelectrons. The interference between these photoelectrons leads to unique curved interference fringes which are observable for most current intense field experiments, opening another way to record the electron dynamics in atoms and molecules on a time scale much shorter than an optical cycle.

We have developed a cold atom Sagnac interferometer with a single large Raman beam. In combination with a time-of-flight measurement performed by thin probe beams, the variation in spatial contrast of the atomic Mach-Zehnder interference was analyzed by considering the spatial intensity profile of the single large Raman beam and the spatial density profile of the atomic cloud. Based on our analysis, we determined that contrast enhancement is attainable using the spatial selection of the atomic cloud but it reduces angular velocity sensitivity.

The nonlinear optical response of a system of molecules often contains contributions whereby the products of lower-order processes in two separate molecules give signals that appear on top of a genuine direct higher-order process with a single molecule. These many-body contributions are known as cascading and complicate the interpretation of multidimensional stimulated Raman and other nonlinear signals. In a quantum electrodynamic treatment, these cascading processes arise from second-order expansion in the molecular coupling to vacuum modes of the radiation field, i.e., single-photon exchange between molecules, which also gives rise to other collective effects. We predict the relative phase of the direct and cascading nonlinear signals and its dependence on the microscopic dynamics as well as the sample geometry. This phase may be used to identify experimental conditions for distinguishing the direct and cascading signals by their phase. Higher-order cascading processes involving the exchange of several photons between more than two molecules are discussed.

Optical parametric phase (OPP), inherently induced in optical parametric chirped-pulse amplification (OPCPA), will significantly degrade pulse compression in the few-cycle pulse regime. While OPP is a well-known nonlinear phenomenon, its nonlinearity origin has remained unclear in physics. Here, we present a systematic theoretical investigation on OPP and demonstrate that OPP originates from the cascaded quadratic nonlinearity in a broadband OPCPA with intrinsic phase-mismatch. Because the intrinsic phase-mismatch is frequency dependent, OPP manifests itself as a nonlinear spectral phase. We show that OPP increases with the parametric gain, approaches to half the intrinsic phase-mismatch in the high-gain limit, and thus directly links with the crystal dispersion. We also find that the effect of OPP in the spatial domain is typically negligible, which makes the OPP compensation necessary only in the spectral domain. The results presented in this paper are of importance to guide the design of few-cycle intense OPCPA systems.

In this paper we construct a type of cavity array, in each cavity of which multiple two-level atoms interact with two independent photon modes. This system can be totally governed by a two-mode Dicke-lattice model, which includes all of the counter-rotating terms and therefore works well in the ultrastrong coupling regime achieved in recent experiments. Attributed to its special atom-photon coupling scheme, this model supports a global conserved excitation and a continuous U(1) symmetry, rather than the discrete $Z_2$ symmetry in the standard single-mode Dicke-lattice model. This distinct change of symmetry via adding an extra photon mode strongly impacts the nature of photon localization and delocalization behavior. Specifically, the atom-photon interaction features stable Mott-lobe structures of photons and a second-order superfluid–Mott-insulator quantum phase transition, which share similarities with the Jaynes-Cummings-lattice and Bose-Hubbard models. More interestingly, the Mott-lobe structures predicted here depend crucially on the atom number of each site. We also show that our model can be mapped into a continuous $XX$ spin model. Finally, we propose a scheme to implement the introduced cavity array in circuit quantum electrodynamics. This work broadens our understanding of strongly correlated photons.

Most of existing protocols for the decoy-state measurement-device-independent quantum key distribution use vacuum sources or extremely weak sources, but the laboratory cannot give real vacuum sources or precise extremely weak sources. We present a four-intensity protocol without using any of them. Our protocol gives a secure key rate close to those in the protocols with vacuum sources.

The concept of correlation is central to all approaches that attempt the description of many-body effects in electronic systems. Multipartite correlation is a quantum information theoretical property that is attributed to quantum states independent of the underlying physics. In quantum chemistry, however, the correlation energy (the energy not seized by the Hartree-Fock ansatz) plays a more prominent role. We show that these two different viewpoints on electron correlation are closely related. The key ingredient turns out to be the energy gap within the symmetry-adapted subspace. We then use a few-site Hubbard model and the stretched ${\mathrm{H}}_2$ to illustrate this connection and to show how the corresponding measures of correlation compare.

We study the dynamics of a set of two-level systems coupled by dipolar interactions under a resonant external Rabi drive. The two-level systems are prepared initially in a coherent product state, and we ask how the nonequilibrium conditions caused by the drive affect this coherence. We study the full nonlinear dynamics of the coupled two-level systems within a classical approximation by analyzing numerically the equations of motion and determining the stability of the collective coherent state within classical Floquet theory. We establish the behavior analytically in the high Rabi coupling limit by employing a Magnus expansion and spin-wave analysis. Our results show that, typically, the dipole interactions between the two-level systems lead to instabilities that cause a breakdown of the collective Rabi oscillations. However, we identify parameter regimes for which the two-level systems undergo collective coherent Rabi oscillations even in the presence of the dipole interactions.

The propagation, storage, and release of two quantized light fields in an optically dressed atomic medium in the tripod configuration are studied. Using the formalism of spinor dark-state polaritons, the probabilities are obtained of finding outgoing photons of two possible localizations and two possible types, i.e., having different frequencies or polarizations. An additional interaction at the storage stage is applied which modifies the atomic coherences due to the stored photons; this results in a modification of the states of the outgoing photons. The conditions are examined for the photons' spatial and type coalescence typical of the Hong-Ou-Mandel effect, i.e., a zero probability of finding the outgoing photons having not only different localizations but also types. These results can possibly be observed in rubidium vapors.

We present a quantum theory of parametric down-conversion of light in chirped quasi-phase-matched second-order nonlinear crystals with undepleted quasimonochromatic pump. This theory allows us to consider generation of ultrabroadband squeezed states of light and is valid for arbitrary, sufficiently slowly varying nonlinear poling profiles. Using a first-order approximate quantum solution for the down-converted light field, we calculate the squeezing spectra and the characteristic squeezing angles. We compare the approximate solutions with the exact and numerical ones and find a very good agreement. This comparison validates our approximate solution in the regime of moderate gain, where the existing approaches are not applicable. Our results demonstrate that aperiodically poled crystals are very good candidates for generating ultrabroadband squeezed light with the squeezing bandwidth covering almost all the optical spectrum and the correlation time approaching a single optical cycle.