A method is presented for precise calculation of the energy corrections due to second-order electric-quadrupole interactions, as well as mixed electric quadrupole-vacuum polarization in the framework of the dynamic hyperfine structure in heavy muonic atoms. For this, a multipole expansion of the Uehling potential is performed. The approach is applicable for an arbitrary nuclear electric charge distribution. By performing these calculations for muonic rhenium and uranium using a deformed Fermi distribution, it is shown that both corrections contribute on a level presumably visible in upcoming experiments.

We theoretically investigate correlated electron dynamics in high-order harmonic generation, using all-electron ab initio simulations for three-dimensional real alkali-metal atoms. The resulting harmonic spectra exhibit a plateau extended beyond the usual cutoff and a prominent resonance peak above the plateau. These remarkable features arise from the cation response dramatically enhanced by laser-induced electron recollision, which is a key process of attosecond science. This demonstrates that high-order harmonic spectroscopy provides possibilities to explore dynamical electron correlation in strong laser pulses.

The Larkin-Ovchinnikov (LO) state which combines the superfluidity and spatial periodicity of pairing order parameters and exhibits supersolid properties has been attracting intense attention in both condensed-matter physics and ultracold atoms. Conventionally, realization of the LO state from an intrinsic $s$-wave interacting system necessitates breaking the time-reversal (TR) and sometimes spatial-inversion (SI) symmetries. Here we report a prediction that the LO state can be realized in a TR- and SI-symmetric system representing a bilayer Fermi gas subjected to a laser-assisted interlayer tunneling. We show that the intralayer $s$-wave atomic interaction acts effectively like a $p$-wave interaction in the pseudospin space. This provides distinctive pairing effects in the present system with pseudspin spin-orbit coupling, and leads to a spontaneous density modulation of the pairing order predicted in a very broad parameter regime. Unlike the conventional schemes, our results do not rely on the spin imbalance or external Zeeman fields, showing a highly feasible way to observe the long-sought-after LO superfluid phase using the laser-assisted bilayer Fermi gases.

The scrambling rate ${\lambda }_L$ associated with the exponential growth of out-of-time-ordered correlators can be used to characterize quantum chaos. Here we use a particular Majorana fermion representation of spin-$1/2$ systems to study quantum chaos in the Dicke model. We take the system to be in thermal equilibrium and compute ${\lambda }_L$ throughout the phase diagram to leading order in $1/N$. We find that the chaotic behavior is strongest close to the critical point. At high temperatures ${\lambda }_L$ is nonzero over an extended region that includes both the normal and superradiant phases. At low temperatures ${\lambda }_L$ is nonzero in (a) close vicinity of the critical point and (b) a region within the superradiant phase. In the process we also derive an effective theory for the superradiant phase at finite temperatures. Our formalism does not rely on the assumption of total spin conservation.

We show violations of Leggett-Garg inequalities to be possible for single-mode cat states evolving dynamically in the presence of a nonlinear quantum interaction arising from, for instance, a Kerr medium. In order to prove the results, we derive a generalized version of the Leggett-Garg inequality involving different cat states at different times. The violations demonstrate failure of the premise of macrorealism as defined by Leggett and Garg, provided extra assumptions associated with experimental tests are valid. With the additional assumption of stationarity, violations of the Leggett-Garg inequality are predicted for the multicomponent cat states observed in the Bose-Einstein condensate and superconducting circuit experiments of Greiner et al. [Nature (London) 419, 51 (2002)] and Kirchmair et al. [Nature (London) 495, 205 (2013)]. The violations demonstrate a mesoscopic quantum coherence, by negating that the system can be in a classical mixture of mesoscopically distinct coherent states. Higher orders of nonlinearity are also studied and shown to give strong violation of Leggett-Garg inequalities. Loopholes for testing macrorealism are discussed.

We explore the question as to whether quantum effects can yield a speedup of the nonequilibrium evolution of fully connected quadratic spin models towards a classical thermal state. In our approach we exploit the fact that the thermal state of a spin system can be mapped onto a node-free quantum state whose coefficients are given by thermal weights. This perspective permits the construction of a dissipative yet quantum dynamics which encodes in its stationary state the thermal state of the original problem. We show for the case of an all-to-all connected Ising spin model that an appropriate transformation of this dissipative dynamics allows us to interpolate between a regime in which the order parameter obeys the classical equations of motion under Glauber dynamics and a quantum regime with an accelerated transient timescale before approaching stationarity. We show that this effect enables, in principle, a speedup of pattern retrieval in a Hopfield neural network.

We present a hybrid quantum repeater protocol for the long-distance distribution of atomic entangled states beyond qubits. In our scheme, imperfect noisy entangled pairs of two qudits, i.e., two discrete-variable $d$-level systems, each of, in principle, arbitrary dimension $d$, are initially shared between the intermediate stations of the channel. This is achieved via local, sufficiently strong light-matter interactions, involving optical coherent states and their transmission after these interactions, and optical measurements on the transmitted field modes, especially efficient continuous-variable homodyne detections (“hybrid” here refers to the simultaneous exploitation of discrete- and continuous-variable degrees of freedom for the local processing and storage of entangled states as well as their nonlocal distribution, respectively) and unambiguous state discrimination. For qutrits we quantify the light-matter entanglement that can be effectively shared through an elementary lossy channel, and for a repeater spacing of up to 10 km we show that the realistic (lossy) qutrit entanglement is even larger than any ideal (loss-free) qubit entanglement. After including qudit entanglement purification and swapping procedures, we calculate the long-distance entangled-pair distribution rates and the final entangled-state fidelities for total communication distances of up to 1280 km. For example, employing unambiguous state discrimination, with three rounds of purification, entangled qudit pairs of near-unit fidelity can be distributed over 1280 km at an ideal maximal rate (assuming perfect gate operations) on the order of 100 Hz.

We consider quantum communication schemes where quantum optical signals are exchanged between a source on Earth and a satellite. The background curved spacetime affects the quantum state of the propagating photons. We employ quantum-metrology techniques to obtain optimal bounds for the precision of quantum measurements of relevant physical parameters encoded in the final state. We focus on satellites in low Earth orbits and we find that our scheme improves the precision of the measurement of the Schwarzschild radius obtained within previous studies. Therefore, our techniques can provide the theoretical tools for novel developments that can potentially outperform the state-of-the-art obtained through classical means. We also review the impact of the relativistic effects on a simple quantum key distribution protocol within satellite schemes and find that such effects can be greatly damaging if they are not properly accounted for.

Explicitly correlated calculations of interaction energies with wave functions that include all interparticle distances have suffered so far from the lack of size consistency resulting from the difficulty of defining monomer energies corresponding to the applied dimer basis. As a consequence, it has not been possible to obtain interaction energies vanishing at infinite intermonomer distance $R$. This has dramatically reduced the accuracy of calculations at distances where the error in the dimer energy was comparable with the interaction energy itself. The same problem occurs in calculations of interaction-induced properties. In this paper, we show how to circumvent this difficulty and obtain interaction energies or interaction-induced properties that vanish at large $R$. This is achieved by relaxing the Pauli principle in the diagonalization of the Hamiltonian of noninteracting monomers. The basis functions used for this diagonalization belong to the representation of the permutation group of the dimer induced by the product of representations appropriate for the monomer spin states. Nonlinear parameters of the basis set are optimized only for the dimer in the Pauli-allowed sector of the Hilbert space. In this way, one obtains $R$-dependent energy of noninteracting monomers and the corresponding interaction energy includes a counterpoise correction for the basis set superposition error. The efficiency of this procedure is demonstrated for the interaction of two hydrogen atoms where accurate reference data are known.

A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains in the quasi-one-dimensional confinement is shown. Additionally, fragmentation of a BEC has been observed outside confinement, in free space. In the end a double BEC production setup for studying soliton collisions is described.

Time crystals are quantum systems that are able to reveal condensed matter behavior in the time domain. It is known that crystallization in time can be observed in a periodically driven many-body system when interactions between particles force a system to evolve with a period that is an integer multiple of a driving period. This phenomenon is dubbed discrete time crystal formation. Here, we consider ultracold atoms bouncing on an oscillating atom mirror and show that the system can spontaneously form a discrete time crystal where the ratio of a period of its motion and a driving period is a rational number. This kind of discrete time crystal requires higher-order resonant driving, which is analyzed here with the help of an original approach.

Fiber-optic multioctave supercontinuum generation is a unique resource for ultrafast optical science, enabling ultrabroadband frequency-comb technologies and paving the way for the photonics of subcycle field wave forms. Extension of these methods to the midinfrared spectral range encounters numerous challenges, calling for radically new approaches in fiber optics and short-pulse generation technologies, as well as for closing the gaps in our understanding of optical nonlinearities in the midinfrared range. Here, we confront these challenges by showing that multioctave supercontinua spanning from the ultraviolet to the midinfrared range can be generated by shock-wave-coupled soliton self-compression of ultrashort midinfrared pulses in a gas-filled antiresonance-guiding hollow-core photonic-crystal fiber. Analysis of the fiber output spectra, measured within a broad range of gas pressures and input driver energies, shows that multioctave supercontinuum generation in this setting becomes possible due to soliton self-compression coupled to shock-wave pulse self-steepening, yielding extraordinarily short, sub-half-cycle field transients.

Master equations are typically adopted to describe the dynamics of open quantum systems. Such equations are either in integro-differential or in time-local form, with the latter class more frequently adopted due to the simpler numerical methods developed to obtain the corresponding solution. Here we show that any time-local master equation with positive rates in the generator, i.e., any completely positive divisible quantum process, admits a microscopic model whose reduced dynamics is well described by the given equation.

We propose a method to continually monitor the energy of a quantum system. We show that by having some previous knowledge of the system's dynamics, but not all of it, one can use the measured energy to determine many other quantities, such as the work performed on the system, the heat exchanged between the system and a thermal reservoir, the time dependence of the Hamiltonian of the system as well as the total entropy produced by its dynamics. We have also analyzed how this method is dependent on the quality factor of the measurements employed.

Recent development of mixed-state encoding (MSE) allows pure-state logical information to be encoded by a bosonic (continuous-variable) system in mixed physical state. Despite interest due to its counterintuitiveness, the utility of the current MSE scheme is limited due to several operational drawbacks, namely redundant information carrier, probabilistic initialization, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state bosonic mode and the logical basis can be deterministically initialized from thermal equilibrium. All logical operations of this encoding can be performed with continuous-variable interaction and measurement only. Without the necessity of ground-state cooling, our proposal could broaden the set of candidate systems for implementing quantum computers and reduce the reliance on demanding refrigerating facility for current quantum computing architectures. Additionally, our protocol can enhance the noise tolerance of logical qubit even if the system can be efficiently cooled.

We study the distinguishability of a particular type of maximally entangled states—the “lattice states”—using an approach of a semidefinite program. With this, we successfully construct all sets of four ququad-ququad orthogonal maximally entangled states that are locally indistinguishable and find some curious sets of six states having an interesting property of distinguishability. Also, some of the problems that arose from Cosentino and Russo [Quantum Inf. Comput. 14, 1098 (2013)] about the positive-partial-transpose distinguishability of lattice maximally entangled states can be answered.

Quantum-enhanced parameter estimation has widespread applications in many fields. An important issue is to protect the estimation precision against the noise-induced decoherence. Here we develop a general theoretical framework for improving the precision for estimating an arbitrary parameter by monitoring the noise-induced quantum trajectories (MQT) and establish its connections to the purification-based approach to quantum parameter estimation. Monitoring the noise-induced quantum trajectory can be achieved in two ways: (i) Any quantum trajectories can be monitored by directly monitoring the environment, which is experimentally challenging for realistic noises, and (ii) certain quantum trajectories can also be monitored by frequently measuring the quantum probe alone via ancilla-assisted encoding and error detection. This establishes an interesting connection between MQT and the full quantum-error-correction protocol. Application of MQT to estimate the level splitting and decoherence rate of a spin 1/2 under typical decoherence channels demonstrate that it can avoid the long-time exponential loss of the estimation precision and, in special cases, recover the Heisenberg scaling.

Quantum state transfer is a basic task for quantum information processing, which can be easily executed using the coherent dynamics for a closed system instead of the dissipative dynamics for an open system. Here we propose a dissipation-assisted scheme to directionally transfer an arbitrary quantum state from the sender $A$ to the receiver $B$ by virtue of the Rydberg antiblockade mechanism, the laser-induced Raman transition, and the photon loss of an optical cavity. The prominent advantage of the current proposal is that it does not require accurate control over the relevant parameters of the system, as the target state is the steady state of the whole process. The effect of atomic spontaneous emission for the excited states is dramatically restricted by the adiabatic elimination, and a high population of the transferred state around $99\%$ is achievable with the current experimental technology.

Atoms and ions of lanthanides have multiple opens shells along with an open $4f^k$ subshell. This paper studies the effect of electron correlation in such systems and how wave functions can be determined for the accurate prediction of atomic properties in the case of ${\mathrm{Ce}}^{2+}$ where $k=2$, using the multireference single- and double-excitation method. An efficient higher-order method is recommended for more reliable results.