We address in this work the phase sensitivity of a Mach-Zehnder interferometer with Gaussian input states. A squeezed-coherent plus squeezed vacuum input state allows us to unambiguously determine the optimal phase-matching conditions in order to maximize the quantum Fisher information. Realistic detection schemes are described and their performance compared with respect to the quantum Cramér-Rao bound. The core of this paper discusses in detail the most general Gaussian input state, without any a priori parameter restrictions. Prioritizing the maximization of various terms in the quantum Fisher information has the consequence of imposing the input phase-matching conditions. We discuss in detail when each scenario yields an optimal performance. Realistic detection scenarios are also considered and their performance compared to the theoretical optimum. The impact of the beam splitter types employed on the optimum phase-matching conditions is also discussed. We find a number of potentially interesting advantages of these states over the coherent plus squeezed vacuum input case.

This paper describes an integer multiplier for the light orbital angular momentum (OAM) through circular-sector transformations, whereby the cross-sectional circular shape of the OAM mode is geometrically transformed to circular-sector shape. Our method can be simply understood in complex function theory and the transformation process can be visualized as unwrapping a Riemann surface, including multiple sheets into a single sheet. The conversion accuracy is significantly better than the previous method because our method uses single-step geometric transformation. Our method has strong potential for the spatial mode manipulation of OAM and other useful spatial modes.

Arbitrary distributions of radiant exposure may be written by transversely scanning a single known spatially random screen that is normally illuminated by spatially but not necessarily temporally uniform radiation or matter wave fields. The arbitrariness of the written pattern of radiant exposure holds up to both a spatial resolution that is dictated by the characteristic transverse length scale of the illuminated spatially random screen and a background term that grows linearly with the number of random-illumination patterns. Two classes of the method are developed. One assumes the distance between the illuminated random mask and the target plane to be sufficiently small that the effects of diffraction may be neglected. The other accounts for the effects of Fresnel diffraction in the regime of large Fresnel number. Numerical simulations are provided for both variants of the method. Contrast and the signal-to-noise ratio are also considered. The method may be parallelized and is suited to both magnifying and demagnifying geometries. Possible applications include spatial light modulators and intensity projectors for those matter and radiation wave fields for which such devices do not exist, printing or microfabrication in both two and three spatial dimensions, and lithography.

Multiple filamentation of terawatt femtosecond Ti:sapphire laser beams in air is experimentally investigated for intermediate external focusing conditions with the numerical apertures $\mathrm{NA}={10}^{-2}$ and $4\times {10}^{-3}$. The electron density distribution in a multifilament plasma channel is measured by means of transversal interferometry. The results confirm the existence of superdense filaments (superfilaments). It is also found that the maximum electron density in filaments differs by an order of magnitude ($\sim 7\times {10}^{17}{\mathrm{cm}}^{-3}$ and $\sim 9\times {10}^{16}{\mathrm{cm}}^{-3}$) for the two values of NA. This demonstrates high sensitivity of the multiple filamentation regime to focusing conditions. The interferometric results are compared with the spatially resolved measurements of the luminescence intensity from the multifilament plasma channel to verify the accuracy of the widely used luminescence technique.

Electron quantum path interferences in strongly laser-driven aligned molecules and their dependence on the molecular alignment is an essential open problem in strong-field molecular physics. Here, we demonstrate an approach which provides direct access to the observation of these interference processes. The approach is based on the combination of the time-gated-ion-microscopy technique with a pump-probe arrangement used to align the molecules and generate high-order harmonics. By spatially resolving the interference pattern produced by the spatiotemporal overlap of the harmonics emitted by the short and long electron quantum paths, we have succeeded in measuring in situ their phase difference and disclose their dependence on molecular alignment. The findings constitute a vital step towards an understanding of strong-field molecular physics and the development of attosecond spectroscopy approaches without the use of auxiliary atomic references.

We present an in situ study of the electron dynamics of an ultracold ${}^{85}\mathrm{Rb}$ plasma using microwave cavity resonance spectroscopy with submicrosecond temporal resolution and vastly improved sensitivity. We observe a three times faster plasma decay than predicted by a self-similar Gaussian expansion model, which might be attributed to collisional microwave heating and plasma-wall interactions. The demonstrated sensitivity enables nondestructive probing of other (nearly) ionized media of fundamental importance as well, such as cold Rydberg gases and antihydrogen plasmas.

Nonclassicality of light has been studied, both extensively and intensively, in terms of optical coherent states, and various quantifiers for nonclassicality of light have been introduced in recent decades. In contrast, the corresponding quantification issue for atomic spin systems is relatively less studied, though there has been some remarkable progress. In this paper, by virtue of the Wigner-Yanase skew information and working in the framework of atomic coherent states, we introduce a quantifier for nonclassicality of atomic spin states from an information-theoretic perspective and reveal its fundamental properties. This quantifier leads to a simple yet powerful criterion for detecting nonclassicality via convexity of the skew information. This criterion is sufficient, but not necessary. The concept is illustrated through several paradigms. We further elucidate some intrinsic relations between nonclassicality and entanglement and indicate that the nonclassicality quantifier may be transferred to an entanglement quantifier.

Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed-matter physics. Here, we utilize a step-dependent coin in quantum walks and investigate what topological phases we can simulate with it, their topological invariants, bound states, and possibility of phase transitions. These quantum walks simulate nontrivial phases characterized by topological invariants (winding number) $\pm 1$, which are similar to the ones observed in topological insulators and polyacetylene. We confirm that the number of phases and their corresponding bound states increase step dependently. In contrast, the size of topological phase and distance between two bound states are decreasing functions of steps resulting into formation of multiple phases as quantum walks proceed (multiphase configuration). We show that, in the bound states, the winding number and group velocity are ill defined and the second moment of the probability density distribution in position space undergoes an abrupt change. Therefore, there are phase transitions taking place over the bound states and between two topological phases with different winding numbers.

Coherent control of the photoelectron angular distribution (PAD) in ionization by a bichromatic circularly polarized field is theoretically studied in neon in the photon energy range 16–20 eV. The breakdown of the PAD axial symmetry with respect to the light propagation direction is analyzed. The coherent control of the PAD manifests itself through: (1) a change from a one-lobe to a three-lobe shape, respectively, for co- and counter-rotating harmonics, (2) a variation of the polar asymmetry with the light frequency, and (3) a rotation of the PAD around the direction of the beam depending on the relative phase between the harmonics. Tuning the lowest harmonic at the $2p^{5}3s$ or $2p^{5}4s$ intermediate excited states strongly influences the PAD. In contrast to atomic hydrogen and the alkali atoms, the cases of equal and opposite helicity are not related in neon. Features of a conjugate polarization setup, when one harmonic is linearly polarized while the other one is circularly polarized, are also discussed.

We report beyond mean-field many-body calculations of ground-state mass current and superfluid fraction for a system of few bosons confined in a ring geometry in the presence of a rotating weak link induced by a potential barrier. We apply the multiconfiguration Hartree method for bosons to do beyond mean-field calculations of the average superfluid fraction for various barrier heights, interaction strengths, and number of particles. This approach presents us a way to continuously sweep the interaction from a weak to strong case. For different rotating frequencies, the ground-state energy remains periodic but with a different landscape depending on the barrier height, and this periodicity implies a decrease on the mass current for fast rotating barriers. With the rotation frequency close to zero, our results show that by sufficiently increasing the barrier, the superfluid fraction eventually drops to zero regardless of interaction strength and number of particles. Also, the condensate fraction depends almost exclusively on the interaction strength, which shows independence of superfluidity and condensation. We also obtained correlation functions to explain the superfluidity behavior, which is not possible in the mean-field theory. This may be relevant to new devices based on atomtronics.

Using a leading-order semiclassical approximation, we calculate the third- and fourth-order virial coefficients of nonrelativistic spin-1/2 fermions in a harmonic trapping potential in arbitrary spatial dimensions, and as functions of temperature, trapping frequency, and coupling strength. Our simple, analytic results for the interaction-induced changes $\mathrm{\Delta }{b}_3$ and $\mathrm{\Delta }{b}_4$ agree qualitatively, and in some regimes quantitatively, with previous numerical calculations for the unitary limit of three-dimensional Fermi gases.

Following up on recent calculations, we investigate the leading- and next-to-leading-order semiclassical approximation to the virial coefficients of a two-species fermion system with a contact interaction. Using the analytic result for the second-order virial coefficient as a renormalization condition, we derive expressions for up to the seventh-order virial coefficient $\mathrm{\Delta }{b}_7$. Our results at leading order, though approximate, furnish simple analytic formulas that relate $\mathrm{\Delta }{b}_n$ to $\mathrm{\Delta }{b}_2$ for arbitrary dimension, providing a glimpse into the behavior of the virial expansion across dimensions and coupling strengths. As an application, we calculate the pressure and Tan's contact of the two-dimensional attractive Fermi gas and examine the radius of convergence of the virial expansion as a function of the coupling strength.

We consider a possible route to ground-state cooling of a levitated nanoparticle, magnetically trapped by a strong permanent magnet, using a combination of measurement and feedback. The trap frequency of this system is much lower than those involving trapped ions or nanomechanical resonators. Minimization of environmental heating is therefore challenging as it requires control of the system on a timescale comparable to the inverse of the trap frequency. We show that these traps are an excellent platform for performing optimal feedback control via real-time state estimation, for the preparation of motional states with measurable quantum properties.

We prove that superradiant phase transitions (SPTs) of the Dicke model and its generalizations in the thermodynamic and classical oscillator limit are indeed of the same type. In this sense, we unify SPTs under both limits at zero and finite temperature. We show that the mean-field approximation for bosons is exact in both cases, and compute the structure and location of the phase transitions in parameter space using a concise analytic method. Moreover, we illustrate how SPT properties (first order, second order, or none) are related to symmetry. Finally, we uncover general features of the phase structure in the space of parameters of these models with dipolar couplings. There will be a region of normal phase in the neighborhood of the origin of the space of dipolar couplings $\vec{\gamma }$, and that generally one flows radially in this space to a superradiant phase.

The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution function, we convert the Vlasov-Maxwell system into a Hamiltonian simulation problem. Then for the limiting case of electrostatic Landau damping, we design and verify a quantum algorithm, appropriate for a future error-corrected universal quantum computer. While the classical simulation has costs that scale as $O\left(N_{v}t\right)$ for a velocity grid with $N_v$ grid points and simulation time $t$, our quantum algorithm scales as $O[\text{polylog}\left(N_v\right)t/\delta ]$ where $\delta$ is the measurement error, and weaker scalings have been dropped. Extensions, including electromagnetics and higher dimensions, are discussed. A quantum computer could efficiently handle a high-resolution, six-dimensional phase-space grid, but the $1/\delta$ cost factor to extract an accurate result remains a difficulty. This paper provides insight into the possibility of someday achieving efficient plasma simulation on a quantum computer.

A Bayesian approach to quantum process tomography has yet to be fully developed due to the lack of appropriate probability distributions on the space of quantum channels. Here, by associating the Choi matrix form of a completely positive, trace preserving (CPTP) map with a particular space of matrices with orthonormal columns, called a Stiefel manifold, we present two parametric probability distributions on the space of CPTP maps that enable Bayesian analysis of process tomography. The first is a probability distribution that has an average Choi matrix as a sufficient statistic. The second is a distribution resulting from binomial likelihood data that enables a simple connection to data gathered through process tomography experiments. These are examples of continuous, nonunitary random CPTP maps that capture meaningful prior information for use in Bayesian estimation. We show how these distributions can be used for point estimation using either maximum a posteriori estimates or expected a posteriori estimates, as well as full Bayesian tomography resulting in posterior credibility intervals. This approach will enable the full power of Bayesian analysis in all forms of quantum characterization, verification, and validation.

Cross sections for positron scattering from molecular nitrogen are reported for energies below the positronium formation threshold. The elastic and state-to-state rotational and vibrational cross sections were obtained within the close-coupling formalism, using a three-dimensional potential energy surface for the interaction of the system. The inelastic cross sections was involved in a kinetic model to describe recent experimental results about positron cooling in a buffer gas of molecular nitrogen. Unlike a previous model [M. R. Natisin et al., J. Phys. B 47, 225209 (2014)], our prediction attributes a leading role to the $0\to 1$ vibrational excitation of ${\mathrm{N}}_2$.

Based on a generic quantum open system model, we study the geometric nature of decoherence by defining a complex-valued geometric phase through stochastic pure states describing nonunitary, noncyclic, and nonadiabatic evolutions. The ensemble average of the complex geometric phases for the pure stochastic states yields a conventional geometric phase together with an amplitude factor. We show that the decoherence process described by the decaying amplitude can be a geometric quantity independent of the system's dynamics. It is a remarkable fact that the geometric phase of a quantum system can serve as an ideal realization of quantum gates due to its robustness against dynamical errors; however, in this paper we show that, for some open quantum systems, a desirable geometric phase may be accompanied by an unwanted robust geometric decoherence factor. Two exactly solvable models are studied to demonstrate that, while the decoherence is a purely dynamical effect for a dephasing two-level model, the decoherence in a dissipative two-level model can be a geometric process. Finally, we show that such a geometric decoherence effect may be eliminated by a nonperturbative control scheme.

Out-of-time-order correlators (OTOCs) play an increasingly important role in different fields of physics and in particular they provide a way of quantifying information scrambling in quantum many-body systems. We verify that an OTOC can be used to probe an excited-state quantum phase transition (ESQPT) in a quantum many-body system. We examine the dynamical properties of an OTOC in the Lipkin-Meshkov-Glick model, which undergoes an ESQPT, using the exact diagonalization method. We show that the long-time evolution of the proposed OTOC is remarkably different in the different phases of the ESQPT. In consequence, we put the long-time averaged value of the OTOC forward as a possible ESQPT order parameter. Our results highlight the connections between OTOCs and ESQPTs, opening the possibility of using OTOCs for accessing experimentally ESQPTs in quantum many-body systems.