Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under permutations between parties, with only $(N+1)(N+2)/2$ local measurement settings, where $N$ is the number of qubits. We apply the decomposition technique to evaluate the fidelity between an unknown prepared state and any target permutation invariant state. In addition, for some typical permutation invariant states, such as the Dicke state with a constant number of excitations, $m$, we derive a tight linear bound on the number of local measurement settings, $m(2m+3)N+1$. Meanwhile, for the Greenberger-Horne-Zeilinger state, the $W$ state, and the Dicke state, we prove a linear lower bound, $\mathrm{\Theta }\left(N\right)$. Hence, for these particular states, our decomposition technique is optimal.

We examine the effects of an artificial gauge field and finite temperature in a two-dimensional disordered Bose-Hubbard model. The disorder considered is diagonal and quenched in nature. A signature of disorder in the Bose-Hubbard model is the Bose glass phase. Our work shows that the introduction of an artificial gauge field enhances the domain of the Bose glass phase in the phase diagram. Most importantly, the size of the domain can be tuned with the strength of the artificial gauge field. The introduction of finite-temperature effects is essential to relate theoretical results with the experimental realizations. For our studies we use the single-site and cluster Gutzwiller mean-field theories. The results from the latter are more reliable as it better describes the correlation effects. Our results show that the Bose glass phase has a larger domain with the latter method.

We derive an effective Dicke model in momentum space to describe collective effects in the quantum regime of a free-electron laser (FEL). The resulting exponential gain from a single passage of electrons allows the operation of a Quantum FEL in the high-gain mode and avoids the experimental challenges of an x-ray FEL oscillator. Moreover, we study the intensity fluctuations of the emitted radiation, which turn out to be super-Poissonian.

We provide rigorous definitions of various components of the energy budget for scattering of source-induced electromagnetic fields by a finite nonmagnetic object. We use the classical volume-integral-equation (VIE) framework and define power rates in terms of integrals of the Poynting vector over various surfaces, enclosing some or all of the impressed sources, scatterer, and environment (such as a planar multilayered substrate). Thus, we generalize the conventional cross sections and obtain new interrelations analogous to the well-known optical theorem. We rigorously treat the strong singularity of the VIE kernel, but keep derivations accessible to a wide audience. The defined power rates are further related to the decay rate enhancement and apparent quantum yield of an arbitrary emitter, which are the core concepts in nanophotonics, surface-enhanced Raman scattering, and electron energy-loss spectroscopy. We also discuss the practical calculation of the power rates and decay rate enhancements in the framework of the discrete dipole approximation (DDA). In particular, we derive the volume-integral expression for the scattered power and use it to prove the automatic satisfaction of the optical theorem irrespective of the discretization level. Thus, the optical theorem cannot be used as an internal measure of the DDA accuracy.

Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a geometrical structure hidden within the time-dependent Schrödinger equation that provides a simple way to view the entire solution space of pulses that suppress noise errors in a system's evolution. In this framework, any single-qubit gate that is robust against quasistatic noise to first order corresponds to a closed three-dimensional space curve, where the driving fields that implement the robust gate can be read off from the curvature and torsion of the space curve. Gates that are robust to second order are in one-to-one correspondence with closed curves whose projections onto three mutually orthogonal planes each enclose a vanishing net area. We use this formalism to derive examples of dynamically corrected gates generated from smooth pulses. We also show how it can be employed to analyze the noise-cancellation properties of pulses generated from numerical algorithms such as grape. A similar geometrical framework exists for quantum systems of arbitrary Hilbert space dimension.

Out-of-time-order correlators (OTOCs), recently at the center of discussion on quantum chaos, are tools to understand the information scrambling in different phases of quantum many-body systems. We propose a disordered ladder spin model, the XX ladder, which can be designed in a scalable cold atom setup to detect OTOCs with a sign reversal protocol alternative to existing approaches for evolution backward in time. We study both the clean and disordered XX ladder and characterize different phases (ergodic and many-body localized phases) of the model based on the decay properties of OTOCs. The emergent effective lightcone shows sublinear behavior, while the butterfly cones drastically differ from the lightcone via demonstrating superlinear behavior. Based on our results, one can observe how the information scrambling changes in the transition from well-studied one-dimensional spin models to unexplored two-dimensional spin models in a local setting.

We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second Rényi entropy of highly mixed quantum states consisting of up to ten qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in one experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.

We study the joint probability distribution function of the work and the change of photon number of the nonequilibrium process of driving the electromagnetic (EM) field in a three-dimensional cavity with an oscillating boundary. The system is initially prepared in a grand-canonical equilibrium state and we obtain the analytical expressions of the characteristic functions of work distributions in the single-resonance and multiple-resonance conditions. Our study demonstrates the validity of the fluctuation theorems of the grand-canonical ensemble in nonequilibrium processes with particle creation and annihilation. In addition, our work illustrates that, in the high-temperature limit, the work done on the quantized EM field approaches its classical counterpart, while in the low-temperature limit, similar to Casimir effect, it differs significantly from its classical counterpart.

A comparative study of bond rearrangement is reported for the double ionization of three triatomic molecules: carbon dioxide, carbonyl sulfide, and water (${\mathrm{D}}_2\mathrm{O}$). Specifically, we study the formation of the molecular cation ${\mathrm{AC}}^{+}$ from the edge atoms of a triatomic molecular dication ${\mathrm{ABC}}^{2+}$ following double ionization by intense, short (23 fs, 790 nm) laser pulses. The comparison is made using the double ionization branching ratio of each molecule, thereby minimizing differences due to differing ionization rates. The rearrangement branching ratio is highest for water, which has a bent initial geometry, while ${\mathrm{CO}}_2$ and OCS are linear molecules. The angular distribution of $\mathrm{O}{}_2{}^{+}$ fragments arising from ${\mathrm{CO}}_2$ is essentially isotropic, while ${\mathrm{SO}}^{+}$ from OCS and ${\mathrm{D}}_2^{+}$ from ${\mathrm{D}}_2\mathrm{O}$ are aligned with the laser polarization. In the ${\mathrm{CO}}_2$ and ${\mathrm{D}}_2\mathrm{O}$ cases, the angular distributions of the bond rearrangement channels are different from the angular distributions of the dominant dissociative double ionization channels ${\mathrm{CO}}^{+}+{\mathrm{O}}^{+}$ and ${\mathrm{OD}}^{+}+{\mathrm{D}}^{+}$. Only the angular distribution of ${\mathrm{SO}}^{+}$ from OCS is both aligned with the laser polarization and similar to the angular distribution of the largest dissociative channel, ${\mathrm{CO}}^{+}+{\mathrm{S}}^{+}$. The mixed behavior observed from the angular distributions of the different molecules stands in contrast to the relative consistency of the magnitude of the bond rearrangement branching ratio.

We experimentally investigate air lasing emission from singly ionized nitrogen molecules exposed to bicircular two-color (BTC) femtosecond laser pulses. The light driven electron recollision is suppressed in the corotating BTC field as compared to the counter-rotating one. It allows us to straightforwardly examine the role of electron recollision on the air lasing generation by simply changing the rotating sense of the BTC fields. Lasing emission is observed for both corotating and counter-rotating BTC fields without noticeable difference when the rotating sense is switched from one to the other case. It indicates a minor contribution of electron recollision on the air lasing emission. In addition to the well-observed linear polarization, we demonstrate that the polarization of the newborn lasing emission can be remotely manipulated from linear to circular by controlling the polarization of the driving second-harmonic field which at the same time acts as the seed.

The strong-field-driven ionization dynamics of larger, nondiatomic molecules still constitutes a major challenge for a theoretical and numerical description. While a full numerical treatment of all electronic and nuclear degrees of freedom is computationally prohibitive, several approaches exist to model photoelectron spectra employing certain approximations. Among them are classical trajectory methods or the so-called strong-field approximation (SFA). Here we investigate in detail the strong-field ionization dynamics of simple, noncollinear triatomic model systems. For a detailed characterization of the ionization process of our system, we combine quantum dynamical simulations, modified classical trajectory calculations, and extensions of the SFA in order to analyze the complex pattern of the photoelectron momentum distribution. We aim at disentangling the contributions of excited states and the long-range character of the potential. We show that upon interaction with circularly polarized laser fields, the long-range character merely induces a small shift in the spectra, while the contribution of excited states is in several cases essential: in particular in near-infrared laser fields, compared to mid-infrared drivers, and for systems with larger internuclear distances, when excited electronic states are energetically closer. Key modifications are for our trajectory model to explicitly incorporate the numerically obtained tunnel barrier width directly into the ionization rate, thereby enabling a spatially anisotropic ionization rate, and an approximate treatment of the contribution of excited states via the Stark shift. In contrast, for the SFA, it is important to include electronically excited states for the description of the initial state. We also discuss the effect of the carrier-envelope phase on the ionization dynamics, as well as the influence of molecular averaging.

We propose an optimal control algorithm for periodic spin dynamics. This nontrivial optimization problem involves the design of a control field maximizing a figure of merit, while finding the initial and final states of the dynamics, which are not known but are subjected to specific periodic conditions. As an illustrative example, we consider the maximization of the signal-to-noise ratio per unit time of spin systems. In the case of a homogeneous spin ensemble and a very short control duration, we show numerically that the optimal field corresponds to the Ernst angle solution. We investigate the optimal control process for longer control durations and their sensitivity to offset inhomogeneities.

We investigate the lasing thresholds and photon statistics of buried multiple quantum well (MQW) photonic crystal (PhC) lasers with a high spontaneous emission coupling coefficient $\beta$ and a large carrier transparency number $N_0$. Using measured input-output curves and delay-dependent second-order photon correlations $g^{\left(2\right)}\left(\tau \right)$, we estimate that our population inversion threshold is near the kink threshold of the input-output curve, which indicates that the buried MQW PhC lasers operate close to the “lasers without inversion” (intensity jump without inversion) regime proposed by Yamamoto and Björk. With respect to static photon statistics $g^{\left(2\right)}\left(0\right)$, the super-Poissonian photon statistics $g^{\left(2\right)}\left(0\right)>1$ are observed even one order of magnitude above the kink threshold. The super-Poissonian photon statistics are specific to the class-B lasers where the photon decay rate ${\gamma }_c$ is much larger than that of carriers ${\gamma }_{\parallel }$ and the relaxation oscillation occurs. We also propose that the pump power needed to maximize the damping time of the relaxation oscillation could be the noise threshold at which the photon statistics change from thermal to Poissonian.

We study, theoretically and experimentally, electromagnetically induced transparency (EIT) in two different solid-state systems. Unlike many implementations in homogeneously broadened media, these systems exhibit inhomogeneous broadening of their optical and spin transitions typical of solid-state materials. We observe EIT line shapes typical of atomic gases, including a crossover into the regime of Autler-Townes splitting, but with the substitution of the inhomogeneous widths for the homogeneous values. We obtain quantitative agreement between experiment and theory for the width of the transparency feature over a range of optical powers and inhomogeneous linewidths. We discuss regimes over which analytical and numerical treatments capture the behavior. As solid-state systems become increasingly important for scalable and integratable quantum optical and photonic devices, it is vital to understand the effects of the inhomogeneous broadening that is ubiquitous in these systems. The treatment presented here can be applied to a variety of systems, as exemplified by the common scaling of experimental results from two different systems.

Based on the powerful method of network control theory, a complete, classically derived, broadband, analytic dispersion model is presented which describes electric susceptibility for a rigorously physically realizable, dielectric material system with a possible dc conductivity contributor. The analysis results in a susceptibility model constructed entirely from pole-residue groups. As a result, solitary Debye-type poles are not physically supported in the broadband analytic dispersion theory presented in this paper. While previous investigators have focused primarily on modeling susceptibility using only negative complex-conjugate poles, the type found naturally at optical frequencies and above, this analysis was conducted under no such restriction; hence, it is considered unified and should apply to all classical-type susceptibility behavior at all frequencies from dc to daylight, including some of the ultraviolet region where the material-continuum assumption begins to break down. Excluding conductivity due to the absence of any proof of magnetic monopole existence, the model should be equally applicable for modeling magnetic susceptibility dispersion. Based upon a rigorous emphasis on physical realizability, the complete, classical dispersion model is demonstrated by successfully modeling the complex permittivity of liquid water at 25 °C using measurement data from 30 MHz to 1200 THz.

We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration space which drives the collapse in a completely deterministic way. This new variable is equivalent to a set of positions of all the particles, i.e., a set of Bohmian positions, which obey the usual guiding equation of Bohmian theory. Any superposition of quantum states of a macroscopic object occupying different regions of space is projected by a localization process onto the region occupied by the positions. Since the Bohmian positions are well defined in a single realization of the experiment, a space localization into one region is produced. The mechanism is based on the correlations between these positions arising from the cohesive forces inside macroscopic objects. The model introduces two collapse parameters which play a role very similar to those of the Ghirardi-Rimini-Weber (GRW) [Ghirardi et al., Phys. Rev. D 34, 470 (1986)] and continuous spontaneous localization (CSL) [Pearle, Phys. Rev. A 39, 2277 (1989); Ghirardi et al., Phys. Rev. A 42, 78 (1990)] theories. With appropriate values of these parameters, we check that the corresponding dynamics rapidly projects superpositions of macroscopic states localized in different regions of space into a single region, while it maintains a negligible effect in all situations where the predictions of standard quantum dynamics are known to be correct. We briefly speculate about the possible relations with gravity. We then study the evolution of the density operator and a mean-field approximation of the dynamical equations of this model, as well as the change of the evolution of the momentum introduced by the localization process. Possible theoretical interpretations are discussed. Generally speaking, this model introduces a sharper border between the quantum and classical worlds than the GRW and CSL theories and leaves a broader range of acceptable values for the parameters.

We consider a system of two particles, each with large angular momentum $j$, in the singlet state. The probabilities of finding projections of the angular momenta on selected axes are determined. The generalized Bell inequalities involve these probabilities and we study them using statistical methods. We show that most of Bell's inequalities cannot be violated, or are violated only marginally, in the limit $j\to \infty$. The precision required to confirm a violation appears to be difficult to achieve. In practice, the quantum system, in spite of being entangled, becomes indistinguishable from its classical counterpart.

The impossibility of undoing a mixing process is analyzed in the context of quantum information theory. The optimal machine to undo the mixing process is studied in the case of pure states, focusing on qubit systems. Exploiting the symmetry of the problem, we parametrize the optimal machine in such a way that the number of parameters grows polynomially in the size of the problem. This simplification makes the numerical methods feasible. For simple but nontrivial cases, we computed the analytical solution, comparing the performance of the optimal machine with other protocols.

The presence of correlations among constituent quantum systems has great relevance in thermodynamics. Significant efforts have been devoted to investigate the role of correlations in work extraction, among others. Here we derive a bound on the difference between global and local extractable work by unitary operations (ergotropic gap) for bipartite separable states. Violation of this bound necessarily certifies the presence of entanglement. This gap is shown to be a monotone under local operations and classical communication-assisted state transformations for pure bipartite quantum states. Further, we provide a thermo-majorization criterion that is sufficient to compare the single-shot work deficit between two pure bipartite entangled states. The ergotropic gap has an implication in witnessing the dimension of a bipartite quantum state with the same local dimensions. On the other hand, our result gives an operational meaning to the Nielsen-Kempe disorder criterion. We also propose a schematic model to visualize the separability bound and to detect entanglement for a restricted class of quantum states.

A recent experiment [Norte et al. Phys. Rev. Lett. 121, 030405 (2018)] probed the variation of the Casimir force between two closely spaced thin Al films as they transition into a superconducting state, observing a null result. We present here computations of the Casimir effect for superconductors, based on the Mattis-Bardeen formula for their optical response. We show that for the Al system used in the experiment the effect of the transition is over 250 times smaller than the experimental sensitivity, in agreement with the observed null result. We demonstrate that a large enhancement of the effect can be achieved by using a system consisting of a Au mirror and a superconducting NbTiN film. We estimate that the effect of the superconducting transition would be observable with the proposed Au-NbTiN configuration, if the sensitivity of the apparatus could be increased by an order of magnitude.