We theoretically investigate the quantum path interferences in interband transitions in solid high-order harmonic generation. The field strength scaling of the 19th harmonic yield from MgO crystal driven by 1600-nm lasers exhibits a sharp minimum. By solving the semiconductor Bloch equation, we separate the short and long trajectories. Our numerical calculation shows that this minimum originates from the coherent interferences between the short and long trajectories. We also illustrate that the interference minimum depends sensitively on the band dispersion, which can be used to retrieve the band structure accurately. We further report that the two-color fields can select the short or long quantum path effectively by controlling the phase. The yield at the plateau or cutoff region of the harmonic spectra can be enhanced by around one order of magnitude by adding a third harmonic with an intensity of only $10\%$ of the fundamental field. Moreover, an isolated attosecond pulse (IAP) is synthesized by controlling the harmonic trajectories in the two-color scheme. The yield of this IAP is enhanced by one order of magnitude compared with the IAP generated by the single-color scheme.

The adiabatic theory of strong-field ionization of molecules with internuclear motion included into consideration is developed. Two adiabatic regimes in terms of the electronic, nuclear, and laser field timescales are considered. In the first regime, field is the slowest; that is, its timescale is much larger than the electronic and nuclear timescales. The corresponding theory generalizes the adiabatic theory of strong-field ionization of atoms and molecules with frozen nuclei [Phys. Rev. A 86, 043417 (2012)] by treating the internuclear motion on equal footing with the electronic motion. In the second regime, the active electron is the fastest; that is, its timescale is much smaller than that of the nuclei and laser field. The corresponding theory naturally involves the Born-Oppenheimer approximation. The two versions of the adiabatic theory are validated by comparing their predictions with accurate numerical results obtained by solving the time-dependent Schrödinger equation (TDSE) for a model diatomic molecule with one electronic and one internuclear degree of freedom. The adiabatic results are shown to converge to the TDSE results uniformly with respect to the laser field amplitude both in tunneling and over-the-barrier ionization regimes. Two applications of the theory to the analysis of strong-field effects associated with the internuclear motion are discussed.

We investigate the nonequilibrium quantum dynamics of one and two heavy fermionic impurities being harmonically trapped and repulsively interacting with a finite ensemble of majority fermions. A quench of the potential of the majority species from a double-well to a harmonic trap is applied, enforcing its counterflow, which in turn perturbs the impurities. For weak repulsions, it is shown that the mixture undergoes a periodic mixing and demixing dynamics, while stronger interactions lead to a more pronounced dynamical spatial separation. In the presence of correlations, the impurity exhibits an expansion dynamics which is absent in the Hartree-Fock case, resulting in an enhanced degree of miscibility. We generalize our results to different impurity masses and demonstrate that the expansion amplitude of the impurity reduces for a larger mass. Furthermore, we showcase that the majority species is strongly correlated and a phase separation occurs on the two-body level. Most importantly, signatures of attractive impurity-impurity induced interactions mediated by the majority species are identified in the time evolution of the two-body correlations of the impurities, a result that is supported by inspecting their spatial size.

We investigate the mechanisms of control and suppression of prethermalization in $N$-component alkaline-earth-metal gases. To this end, we compute the short-time dynamics of the instantaneous momentum distribution and the relative population for different initial conditions after an interaction quench, accounting for the effect of initial interactions. We find that switching on an interaction that breaks the $\mathrm{SU}\left(N\right)$ symmetry of the initial Hamiltonian, thus allowing for the occurrence of spin-changing collisions, does not necessarily lead to a suppression of prethermalization. However, the suppression will be most effective in the presence of $\mathrm{SU}\left(N\right)$-breaking interactions provided the number of components $N\ge 4$ and the initial state contains a population imbalance that breaks the $\mathrm{SU}\left(N\right)$ symmetry. We also find the conditions on the imbalance initial state that allow for a prethermal state to be stabilized for a certain time. Our study highlights the important role played by the initial state in the prethermalization dynamics of multicomponent Fermi gases. It also demonstrates that alkaline-earth-metal Fermi gases provide an interesting playground for the study and control of prethermalization.

We propose a scheme to enhance the light-matter coupling in a cavity QED system where two $\mathrm{\Lambda }$ atoms are weakly coupled to a single-mode cavity via multiphoton interaction. By introducing a second-order nonlinear (parametric) driving of the cavity, the original $N$-photon exchanges between the atoms, and the cavity can be reduced to either an effective single- or two-photon transition depending on the odevity of $N$, with the effective atom-field interaction strength being significantly enhanced. This results in an $N$-dependent effective coupling strength on top of the exponential enhancement induced only by the parametric driving. As an example, we demonstrate that our proposal can be exploited for the preparation of high-fidelity steady-state entanglement. The proposed scheme could provide a feasible alternative for diverse applications in quantum technologies.

We provide the classification of possible wave structures evolving from initially discontinuous profiles for the photon fluid propagating in a normal dispersion fiber. The dynamics of light fields is described by the generalized Chen-Lee-Liu equation, which belongs to the family of the nonlinear Schrödinger equations with a self-steepening-type term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. This equation is also used in investigations of the dynamics of modulated waves propagating through a single nonlinear transmission network. We describe its periodic solutions and the corresponding Whitham modulation equations. The wave patterns generated by the initial parameter profiles are composed of different building blocks which are presented in detail. It is shown that evolution dynamics in this case is much richer than that for the nonlinear Schrödinger equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity. Our analytic results are confirmed by numerical simulations.

We develop a generic model for a cyclic quantum heat engine that makes it possible to coherently amplify a periodically modulated input signal without the need to couple the working medium to multiple reservoirs at the same time. Instead, we suggest an operation principle that is based on the spontaneous creation of population inversion in incomplete relaxation processes induced by periodic temperature variations. Focusing on Lindblad dynamics and systems with equally spaced energy levels, e.g., qubits or quantum harmonic oscillators, we derive a general working criterion for such cyclic quantum amplifiers. This criterion defines a class of candidates for suitable working media and applies to arbitrary control protocols. For the minimal case of a cyclic three-level amplifier, we show that our criterion is tight and explore the conditions for optimal performance.

The study of memory effects in quantum channels helps in developing characterization methods for open quantum systems and strategies for quantum error correction. Two main sets of channels exist, corresponding to system dynamics with no memory (Markovian) and with memory (non-Markovian). Interestingly, these sets have a nonconvex geometry, allowing one to form a channel with memory from the addition of memoryless channels and vice versa. Here, we experimentally investigate this nonconvexity in a photonic setup by subjecting a single qubit to a convex combination of Markovian and non-Markovian channels. We use both divisibility and distinguishability as criteria for the classification of memory effects, with associated measures. Our results highlight some practical considerations that may need to be taken into account when using memory criteria to study system dynamics given by the addition of Markovian and non-Markovian channels in experiments.

Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth, so that only polynomial measurements are required, even for highly entangled states. After that, a subsequent classical circuit simulator is used to transform the information of the target quantum state from the variational quantum circuit into a familiar format. We demonstrate our method by performing numerical simulations for the tomography of the ground state of a one-dimensional quantum spin chain, using a variational quantum circuit simulator. Our method is suitable for near-term quantum computing platforms, and could be used for relatively large-scale quantum state tomography for experimentally relevant quantum states.

High-precision operation of quantum computing systems must be robust to uncertainties and noises in the quantum hardware. We show that through a game played between the uncertainties (or noises) and the controls, adversarial uncertainty samples can be generated to find highly robust controls through the search for Nash equilibria. We propose a broad family of adversarial learning algorithms, namely a-GRAPE algorithms, which includes two effective learning schemes referred to as the best-response approach and the better-response approach within game-theoretic terminology, providing options for learning highly robust controls. Numerical experiments demonstrate that the balance between fidelity and robustness depends on the details of the chosen adversarial learning algorithm, which can effectively lead to a significant enhancement of control robustness while attaining high fidelity.

Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is a novel protocol that eliminates all possible attacks on the detector side and the necessity of reference-frame alignment in source sides. However, its performance may degrade notably due to statistical fluctuations since more parameters, e.g., yields and error rates for mismatched-basis events, must be accumulated to monitor the security. In this work, we find that the original decoy states method estimates these yields overpessimistically since it ignores the potential relations between different bases. Through jointly processing parameters of different bases, the performance of RFI-MDI-QKD is greatly improved in terms of the secret key rate and achievable distance when statistical fluctuations are considered (the statistical fluctuation analysis is the first step to the final analysis of the finite key size effect). Our results pave an avenue towards practical RFI-MDI-QKD.

We present accurate measurements of the quadrupole S(3) and S(4) transitions of the ${\mathrm{D}}_{2}2-0$ band. Self-perturbed spectra were collected in a wide pressure range with a cavity ring-down spectrometer linked to an optical frequency comb. The results of ab initio quantum scattering calculations were incorporated into the line-shape analysis which was performed using the Hartmann-Tran profile. This approach allowed us to mitigate the collisional systematics and to reach a 900-kHz accuracy of the transition frequencies, which represents a 30-fold improvement compared to previously available data. We also compare our findings with newly calculated transition frequencies that include relativistic and quantum electrodynamics corrections up to ${\alpha }^7$. The differences between theoretical and experimental values for the transition frequencies are 2.2 MHz and 3.3 MHz for the S(3) and S(4) transitions, respectively.

We report measurements of the isotope shifts of two transitions ($4f^{4}6s\to {\left[25044.7\right]}_{7/2}^o$ and $4f^{4}6s\to {\left[25138.6\right]}_{7/2}^o$) in neodymium ions (${\mathrm{Nd}}^{+}$) with hundredfold improved accuracy, using laser spectroscopy of a cryogenically cooled neutral plasma. The isotope shifts were measured across a set of five spin-zero isotopes that spans a nuclear shape transition. We discuss the prospects for further improvements to the accuracy of ${\mathrm{Nd}}^{+}$ isotope shifts using optical clock transitions, which could enable extremely precise tests of King plot linearity for new physics searches.

We calculate the isotope-independent ${\mathrm{Li}}^{+}$-Li potential energy curves for the electronic ground and first excited states. The scattering phase shifts and total scattering cross section for the ${}^7\mathrm{Li}^{+}\text{−}{}^7\mathrm{Li}$ collision are calculated, with an emphasis on the ultralow-energy domain down to the $s$-wave regime. The effect of physically motivated alterations on the calculated potential energy curves is used to determine the bound of accuracy of the low-energy scattering parameters for the ion-atom system. It is found that the scattering length for the $A{}^2{\mathrm{\Sigma }}_u^{+}$ state, $a_u=1325a_0$, is positive and has well-constrained bounds. For the $X{}^2{\mathrm{\Sigma }}_g^{+}$ state, the scattering length, $a_g=20465a_0$, has a large magnitude, as it is sensitive to the restrained change of the potential, due to the presence of a vibrational state in the vicinity of the dissociation limit.

For the direct photodissociation of HD in the second threshold, there are four open channels $\mathrm{H}\left(2s\right)+\mathrm{D}\left(1s\right), \mathrm{H}\left(2p\right)+\mathrm{D}\left(1s\right), \mathrm{D}\left(2s\right)+\mathrm{H}\left(1s\right)$, and $\mathrm{D}\left(2p\right)+\mathrm{H}\left(1s\right)$. We measured the channel branching ratios and found that the ratios oscillate with the wave vectors of the photofragments. However, the population ratios $\left[\mathrm{H}\left(2s\right)\right]/\left[\mathrm{H}\left(2s\right)+\mathrm{D}\left(2s\right)\right]$ and $\left[\mathrm{H}\left(2p\right)\right]/\left[\mathrm{H}\left(2p\right)+\mathrm{D}\left(2p\right)\right]$ are nearly constant ∼0.6. The results can be explained by assuming that the photodissociation in the Franck-Condon region follows mechanisms similar to those of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$, i.e., the excitations are to the $3p\sigma B^{\prime }{}^1{{\mathrm{\Sigma }}_u}^{+}$ and $2p\sigma B{}^1{{\mathrm{\Sigma }}_u}^{+}$ states that are interfered with due to the phase differences between the two states. For HD, near the dissociation limits, the $g-u$ pair states that are valid in the Born-Oppenheimer approximation are mixed almost completely in the corrected adiabatic approximation. A diabatic approximation would thus predict that the ratios $\left[\mathrm{H}\left(2s\right)\right]/\left[\mathrm{H}\left(2s\right)+\mathrm{D}\left(2s\right)\right]$ and $\left[\mathrm{H}\left(2p\right)\right]/\left[\mathrm{H}\left(2p\right)+\mathrm{D}\left(2p\right)\right]$ are 0.5.

We construct and solve semianalytically a pump-probe problem which is defined by an excitation-coupling scheme that engages superpositions of resonance states. The scheme is $|0\rangle \underset{attosecpulse{\omega }_1}{\overset{weak}{\to }}\left(\mathrm{superposition}\mathrm{of}\mathrm{resonances}\right)\underset{femtosecpulse{\omega }_2}{\stackrel{moderatelystrong}{\leftrightarrow }}\left(\mathrm{superposition}\mathrm{of}\mathrm{resonances}\right)$ where $|0\rangle$ is a discrete state. The resonance wave functions are treated rigorously as stationary states in the continuous spectrum. They are energy-normalized and are expressed as linear combinations of localized and scattering components, using the formalism of Fano. The attosecond and femtosecond pulses have central frequencies ${\omega }_1$ and ${\omega }_2$, with ${\omega }_1\gg {\omega }_2$. They are applied with positive (the short XUV pulse peaks after the second pulse) or negative (the short XUV pulse peaks before the second pulse) time delay, $t_D$. The theory is time-dependent and involves many-electron wave functions and matrix elements. Its computational implementation is extremely economic. The application which is reported here treats the excitation of a core-excited superposition of valence-Rydberg autoionizing states of carbon near the $K$-absorption edge by a weak 100 as Gaussian pulse, and their coupling to a higher-lying core-excited autoionizing Rydberg state by an 80 fs Gaussian pulse of intensities of order ${10}^{12}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. State-specific $N$-electron correlated wave functions are used. A number of concrete findings are obtained, demonstrating a variety of channel-dependent photoelectron spectra as functions of the pulse parameters and of the time delay, $t_D$.

We study the emergence of density waves in quasi-one-dimensional dipolar Bose-Einstein condensates (BECs) when the strength of dipole-dipole atomic interactions is periodically varied in time. The proposed theoretical model based on the evolution of small perturbations of the background density allows one to calculate the instability growth rate for an arbitrary set of input parameters, thereby identifying instability regions with respect to density waves. We find that among other modes of the system the roton mode is most effectively excited due to a significant contribution of subharmonics of the excitation frequency. The frequency of temporal oscillations of emerging density waves coincides with half of the driving frequency, which is the hallmark of the parametric resonance and is characteristic of Faraday waves. The possibility to create density waves in dipolar BECs, which can persist after emergence, is demonstrated. The existence of a standing-wave solution of the nonlocal Gross-Pitaevskii equation is revealed from numerical simulations. The effect of three-body atomic interactions, which is relevant to condensates with increased density, upon the properties of emerging waves is analyzed too. Significant modification of the condensate's excitation spectrum owing to three-body effects is shown.

The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature $T_{\mathrm{c}}$ decreases with pairing strength in the BEC regime, where it approaches asymptotically $T_{\mathrm{c}}=\pi an/2m$, with $a$ being the $s$-wave scattering length, and $n$ ($m$) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast-growing (absolute value of the) fermionic chemical potential $\mu$ and pairing gap $\mathrm{\Delta }$, which depends exponentially on the ratio $d/a$. Importantly, $T_{\mathrm{c}}$ at unitarity increases with the lattice constant $d$ and hopping integral $t$. The effect of the van Hove singularity on $T_{\mathrm{c}}$ is identified. The superfluid density exhibits $T^{3/2}$ power laws at low $T$, away from the extreme BCS limit. These predictions can be tested in future experiments.

In this paper, we study the effect of population imbalance and its interplay with pairing strength and lattice effect in atomic Fermi gases in a one-dimensional optical lattice. We compute various phase diagrams as the system undergoes BCS-BEC crossover, using the same pairing fluctuation theory as in Part I of this work [Phys. Rev. A 101, 053617 (2020)]. We find widespread pseudogap phenomena beyond the BCS regime and intermediate temperature superfluid states for relatively low population imbalances. The Fermi surface topology plays an important role in the behavior of $T_{\mathrm{c}}$. For large $d$ and/or small $t$, which yield an open Fermi surface, superfluidity can be readily destroyed by a small amount of population imbalance $p$. The superfluid phase, especially in the BEC regime, can exist only for a highly restricted volume of the parameter space. An open Fermi surface often leads to destruction of the superfluid ground state in the BEC regime. Due to the continuum-lattice mixing, population imbalance gives rise to a new mechanism for pair hopping, as assisted by excessive majority fermions, which may lead to significant enhancement of $T_{\mathrm{c}}$ on the BEC side of the Feshbach resonance, and also render $T_{\mathrm{c}}$ approaching a constant asymptote in the BEC limit, when it exists. Furthermore, we find that not all minority fermions will be paired up in BEC limit, unlike the 3D continuum case. These predictions can be tested in future experiments.