Based on a plausible requirement for the ground-state density, we introduce an alternative one-dimensional (1D) atomic model potential for the 1D simulation of the quantum dynamics of a single active electron atom driven by a strong, linearly polarized few-cycle laser pulse. The form of this density-based 1D model potential also suggests improved parameters for other well-known 1D model potentials. We test these 1D model potentials in numerical simulations of typical strong-field physics scenarios and we find an impressively increased accuracy of the low-frequency features of the most important physical quantities. The structure and the phase of the high-order harmonic spectra also have a very good match to those resulting from the three-dimensional simulations, which enables one to fit the corresponding power spectra with the help of a simple scaling function.

We have theoretically investigated Su-Schrieffer-Heeger chains modeled as optical lattices (OLs) loaded with exciton-polaritons. The chains have been subject to the resonant pumping of the edge site and shaken in either an adiabatic or high-frequency regime. The topological state has been controlled by the relative phases of the lasers constructing the OLs. The dynamic problem of the occupation of the lattice sites and eigenstates has been semiclassically solved. Finally, the analysis of the occupation numbers evolution has revealed that gapless, topologically trivial, and nontrivial chain configurations demonstrate perceptible behavior from both qualitative (occupation pattern) and quantitative (total occupation) points of view.

We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring. Optimal paths are defined by extremizing the global probability density to move between two boundary conditions, and are then expressed as solutions to a Hamiltonian dynamical system. We investigate the onset of chaos in pure-state qubit systems with optimal paths generated by a periodic Hamiltonian. Specifically, chaotic quantum dynamics are demonstrated in a scheme where two noncommuting observables of a qubit are continuously monitored, and one measurement strength is periodically modulated. The optimal quantum paths in this example bear similarities to the trajectories of the kicked rotor, or standard map, which is a paradigmatic example of classical chaos. We emphasize connections with the concept of resonance between integrable optimal paths and weak periodic perturbations, as well as our previous work on “multipaths,” and connect the optimal path chaos to instabilities in the underlying quantum trajectories.

It is proven that the exact excited-state wave function and energy may be obtained by minimizing the energy expectation value of trial wave functions that are constrained only to have the correct nodes of the state of interest. This excited-state nodal minimum principle has the advantage that it requires neither minimization with the constraint of wave-function orthogonality to all lower eigenstates nor the antisymmetry of the trial wave functions. It is also found that the minimization over the entire space can be partitioned into several interconnected minimizations within the individual nodal regions, and the exact excited-state energy may be obtained by a minimization in just one or several of these nodal regions. For the proofs of the theorem, it is observed that the many-electron eigenfunction (excited state as well as ground state), restricted to a nodal region, is equivalent to a ground-state wave function of one electron in a higher-dimensional space; and, alternatively, an explicit excited-state energy variational expression is utilized by generalizing the Jacobi method of multiplicative variation. In corollaries, error functions are constructed for cases for which the nodes are not necessarily exact. The exact nodes minimize the energy error functions with respect to nodal variations. Simple numerical illustrations of the error functions are presented.

An important approach to fault-tolerant quantum computation is protecting logical information using quantum error correction. Usually, logical information is in the form of logical qubits, which are encoded in physical qubits using quantum error correction codes. Compared with qubit quantum computation, fermionic quantum computation has advantages in quantum simulations of fermionic systems, e.g., molecules. In this paper, we show that fermionic quantum computation can be universal and fault tolerant if we encode logical Majorana fermions in physical Majorana fermions. We take a color code as an example to demonstrate the universal set of fault-tolerant operations on logical Majorana fermions, and we numerically find that the fault-tolerance threshold is about $0.8\%$.

The correspondence between classical spin models and quantum states has attracted much attention in recent years. However, it remains an open problem as to which specific spin model a given (well-known) quantum state maps. Here, we provide such an explicit correspondence for an important class of quantum states where a duality relation is proved between classical spin models and quantum Calderbank-Shor-Steane (CSS) states. In particular, we employ graph-theoretic methods to prove that the partition function of a classical spin model on a hypergraph $H$ is equal to the inner product of a product state with a quantum CSS state on a dual hypergraph $\tilde{H}$. We next use this dual correspondence to prove that the critical behavior of the classical system corresponds to a relative stability of the corresponding CSS state to bit-flip (or phase-flip) noise, thus called critical stability. We finally conjecture that such critical stability is related to the topological order in quantum CSS states, thus providing a possible practical characterization of such states.

Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an “initiator” graph with itself, have risen in popularity in network science due to their ability to generate complex networks with real-world properties. We explore spatial search by continuous-time quantum walk on Kronecker graphs. Specifically, we give analytical proofs for quantum search on first-, second-, and third-order Kronecker graphs with the complete graph as the initiator, showing that search takes Grover's $O\left(\sqrt{N}\right)$ time. Numerical simulations indicate that higher-order Kronecker graphs with the complete initiator also support optimal quantum search.

Standard quantum tomography of a single qudit achieves an infidelity that scales in the worst case as $O(1/\sqrt{N})$ for a sample of size $N$. Here, we propose a suitable generalization of the two-stage adaptive quantum tomography for a qubit to the case of a single qudit. This achieves an infidelity of the order of $O[1/\sqrt{N_0(N-N_0)}]$ for all quantum states, where $N_0$ and $N-N_0$ are the ensemble sizes employed in the two stages of the method. This result is based on a second-order Taylor series expansion of the infidelity that is obtained by means of the Fréchet derivative and measurement outcomes modeled by a multinomial distribution. Numerical simulations indicate that the choice $N_0=N/2$ leads to an infidelity that scales approximately as $O(1/N)$ for all quantum states in a wide range of dimensions, that is, a quadratic improvement of the infidelity when compared to standard quantum tomography in the case of low-rank states.

We consider discrete-alphabet encoding schemes for coherent-state quantum key distribution. The sender encodes the letters of a finite-size alphabet into coherent states whose amplitudes are symmetrically distributed on a circle centered in the origin of the phase space. We study the asymptotic performance of this phase-encoded coherent-state protocol in direct and reverse reconciliation assuming both loss and thermal noise in the communication channel. In particular, we show that using just four phase-shifted coherent states is sufficient for generating secret-key rates of the order of $4\times {10}^{-3}$ bits per channel use at about 15 dB loss in the presence of realistic excess noise.

Schlömilch's formula is generalized and applied to the thermal Casimir effect of a fermionic field confined to a three-dimensional rectangular box. The analytic expressions of the Casimir energy and Casimir force are derived for arbitrary temperature and edge sizes. The low- and high-temperature limits and finite-temperature cases are considered for the entire parameter space spanned by edge sizes and/or temperature. In the low-temperature limit, it is found that for typical rectangular box, the effective two-dimensional parameter space spanned by the two edge-size ratios can be split into four regions. In one region, all three forces between three pairs of faces are attractive, and in another two regions, the force along the longest edge becomes repulsive, and in the last region the force along both the longest and medium sized edges becomes repulsive. Three forces cannot be made simultaneously repulsive. For the waveguide under low temperature, the Casimir force along the longer side of the waveguide cross section transforms from attractive to repulsive when the aspect ratio of the cross section exceeds a critical value. For the parallel plate scenario under low temperature, our results agree with previous works. For high-temperature limit, it is shown that both the Casimir energy and force approach zero due to the high-temperature suppression of the quantum fluctuation responsible for the Casimir energy. For the finite-temperature case, we separate the parameter space into four subcases (C1–C4) and various edge-size and temperature effects are analyzed. In general, we found that in all cases the Casimir energy is always negative, while the Casimir force at any finite or low temperature can be either repulsive or attractive depending on the sizes of the edges. For the case (C1) that is similar to parallel plates with relatively high temperature, it is found that the Casimir force is always attractive, regardless the change of the plate separation. At the given temperature, the Casimir energy and force densities approach the infinite parallel plate limit even when the plate edge size is two times the plate separation. For the case (C2) that is similar to a waveguide with relatively high temperature, the Casimir force along the longer side of the waveguide cross section transforms from attractive to repulsive when this side exceeds a critical value. This critical point forms a boundary in the parameter space when the shorter edge of the waveguide cross section changes and the boundary values decrease with respect to temperature increase. Case (C3) covers the low-temperature parallel plate, typical rectangular box, and waveguide geometries. For the waveguide case, the force along the waveguide longitude also transforms from attractive to repulsive when the waveguide length exceeds certain critical values. These critical values change with respect to temperature in a nontrivial way. For the typical waveguide case (C4) at low temperature, the Casimir energy density along the longitudinal direction is a constant while force density decreases linearly as the waveguide length increases. Finally, for any fixed temperature, there exists a boundary in the parameter space of edge sizes separating the attractive and repulsive regions. Besides, the Casimir energy for an electromagnetic field confined in a three-dimensional box is also derived.

Three earlier relativistic coupled-cluster (RCC) calculations of dipole polarizability (${\alpha }_d$) of the Cd atom are not in good agreement with the available experimental value of $49.65\left(1.65\right)e{a}_0^3$. Among these two are finite-field approaches in which the relativistic effects have been included approximately, while the other calculation uses a four-component perturbed RCC method. However, another work adopting an approach similar to the latter perturbed RCC method gives a result very close to that of experiment. The major difference between these two perturbed RCC approaches lies in their implementation. To resolve this ambiguity, we have developed and employed the relativistic normal coupled-cluster (RNCC) theory to evaluate the ${\alpha }_d$ value of Cd. The distinct features of the RNCC method are that the expression for the expectation value in this approach terminates naturally and that it satisfies the Hellmann-Feynman theorem. In addition, we determine this quantity in the finite-field approach in the framework of a four-component relativistic coupled-cluster theory. Considering the results from both approaches, we arrive at a reliable value of ${\alpha }_d=46.02\left(50\right)e{a}_0^3$. We also demonstrate that the contribution from the triples excitations in this atom is significant.

We present a protocol for an atomic interferometer that reaches the Heisenberg limit (HL), within a factor of $\sim \sqrt{2}$, via collective state detection and critical tuning of one-axis twist spin squeezing. It generates a Schrödinger cat state, as a superposition of two extremal collective states. When this Schrödinger-cat-state interferometer is used as a gyroscope, the interference occurs at an ultrahigh Compton frequency, corresponding to a mesoscopic single object with a mass of $Nm$, where $N$ is the number of particles in the ensemble, and $m$ is the mass of each particle. For ${}^{87}\mathrm{Rb}$ atoms, with $N={10}^6$, for example, the interference would occur at a Compton frequency of $\sim 2\times {10}^{31}$ Hz. Under this scheme, the signal is found to depend critically on the parity of $N$. We present two variants of the protocol. Under protocol A, the fringes are narrowed by a factor of $N$ for one parity, while for the other parity the signal is zero. Under protocol B, the fringes are narrowed by a factor of $N$ for one parity, and by a factor of $\sqrt{N}$ for the other parity. Both protocols can be modified in a manner that reverses the behavior of the signals for the two parities. Over repeated measurements under which the probability of being even or odd is equal, the averaged sensitivity is smaller than the HL by a factor of $\sim \sqrt{2}$ for both versions of the protocol. We describe an experimental scheme for realizing such an atomic interferometer, and discuss potential limitations due to experimental constraints imposed by the current state of the art, for both collective state detection and one-axis-twist squeezing. We show that when the Schrödinger-cat-state interferometer is configured as an accelerometer, the effective two-photon wave vector is enhanced by a factor of $N$, leading to the same degree of enhancement in sensitivity. We also show that such a mesoscopic single object can be used to increase the effective base frequency of an atomic clock by a factor of $N$, with a sensitivity that is equivalent to the HL, within a factor of $\sim \sqrt{2}$.

We study the dynamics of an interacting Bose-Hubbard chain coupled to a non-Markovian environment. Our basic tool is the reduced generating functional expressed as a path integral over spin-coherent states. We calculate the leading contribution to the corresponding effective action, and by minimizing it, we derive mean-field equations that can be numerically solved. With this tool at hand, we examine the influence of the system's initial conditions and interparticle interactions on the dissipative dynamics. Moreover, we investigate the presence of memory effects due to the non-Markovian environment.

The study of finite-temperature dynamics of one-dimensional Fermi gases is a challenging problem. These systems can present different phenomena, including the formation and propagation of shock waves and collective oscillations. Here we calculate the dynamics of collective oscillations and shock waves in a noninteracting one-dimensional ultracold Fermi gas, at both zero and finite temperature. These results are obtained using the Majorana P-function method, which is a positive phase-space representation on a space of antisymmetric matrices. At zero temperature, the results are in agreement with previous results, where the shock wave is observed as a discontinuity of the density of atoms. At finite temperature, the formation of shock waves is observed but with the shock fronts smoothed out. This places constraints on the experimental observation of shock-wave propagation in a noninteracting Fermi gas or strongly interacting Bose gas.

We study the Floquet edge states in arrays of periodically curved optical waveguides described by the modulated Su-Schrieffer-Heeger model. Beyond the bulk-edge correspondence, our study explores the interplay between band topology and periodic modulations. By analyzing the quasienergy spectra and Zak phase, we reveal that, although topological and nontopological edge states can exist for the same parameters, they cannot appear in the same spectral gap. In the high-frequency limit, we find analytically all boundaries between the different phases and study the coexistence of topological and nontopological edge states. In contrast to unmodulated systems, the edge states appear due to either band topology or modulation-induced defects. This means that periodic modulations may not only tune the parametric regions with nontrivial topology, but may also support novel edge states.

We report two effects in an inhomogeneous ensemble of two-level systems driven by an external field. First, we observe a rigidity of the oscillation frequency: the dominant Rabi oscillation frequency does not change with the frequency of the driving field, in contrast to the well-known law of Rabi frequency increase with growing detuning of the driving field. Second, we observe a time-dependent frequency shift of the ensemble-averaged oscillation. We show that these effects follow from the inhomogeneity of the two-level splitting across the ensemble, allowing for a distribution of local oscillations in which those with high frequencies interfere destructively and decay faster than those with a low frequency, which are the only ones to survive in the output signal. Hence, coherence emerges from long-lived oscillations in an inhomogeneous ensemble. We analyze the Fourier spectrum of the time-dependent oscillation signal and find a nontrivial spectral structure that is double peaked for certain parameters. We show that the effects observed in alkali vapor are universal and expected in any system with a moderate inhomogeneity driven by an external field.

A method for generating terahertz (THz) necklace beams from two-color vortex-laser-induced air plasma is proposed and theoretically investigated based on the frequency down-conversion process. The numerical demonstrations based on both the four-wave mixing and the photocurrent schemes confirm that the generated THz pulse is a shear necklace beam without orbital angular momentum (OAM), whose phase is manifested as the stepwise jump versus azimuthal angle. The origin of OAM vanishing is attributed to the fact that the phase difference between two-color field components does not contribute to the phase but only to the amplitude of the THz pulse.

Motivated by the question whether the empirical fitting of data by neural networks can yield the same structure of physical laws, we apply neural networks to a quantum-mechanical two-body scattering problem with short-range potentials—a problem that by itself plays an important role in many branches of physics. After training, the neural network can accurately predict $s$-wave scattering length, which governs the low-energy scattering physics. By visualizing the neural network, we show that it develops perturbation theory order by order when the potential depth increases, without solving the Schrödinger equation or obtaining the wave function explicitly. The result provides an important benchmark to the machine-assisted physics research or even automated machine learning physics laws.

Using the asymptotic Bethe ansatz, we study the stabilization problem of the one-dimensional spin-polarized Fermi gas confined in a hard-wall potential with a tunable $p$-wave scattering length and finite effective range. We find that the interplay of two factors, i.e., the finite interaction range and the hard-wall potential, will stabilize the system near resonance. The stabilization occurs even on the positive scattering length side, where the system undergoes a many-body collapse if any of the factors is absent. At $p$-wave resonance, the fermion system is found to feature “quasiparticle condensation” for any value of effective range, which is stabilized if the range is above twice the mean particle distance. Slightly away from resonance, the correction to the stability condition linearly depends on the inverse scattering length. Finally, a global picture is presented for the energetics and stability properties of fermions from the weakly attractive to deep bound-state regime. Our results raise the possibility of achieving stable $p$-wave superfluidity in quasi-one-dimensional (1D) atomic systems, and meanwhile shed light on the intriguing $s$- and $p$-wave physics in 1D that violate the Bose-Fermi duality.

We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e., the open dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed “ancillas,” which are subsequently traced out. In this setting, non-Markovianity is introduced by allowing for additional unitary interactions between the ancillas. For this model, we identify the relevant system-environment correlations that lead to a non-Markovian evolution. Through an equivalent picture of the open dynamics, we introduce the notion of “memory depth” where these correlations are established between the system and a suitably sized memory rendering the overall system+memory evolution Markovian. We extend our analysis to show that while most system-environment correlations are irrelevant for the dynamical characterization of the process, they generally play an important role in the thermodynamic description. Finally, we show that under an energy-preserving system-environment interaction, a nonmonotonic time behavior of the heat flux serves as an indicator of non-Markovian behavior.