Positivity preserving density matrix minimization at finite temperatures via square root.

We present a Wave Operator Minimization (WOM) method for calculating the Fermi-Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction using the wave operator, i.e., the square root of the density matrix. WOM models cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. Additionally, we show that the number of steps required for convergence is independent of the number of atoms in the system. We hope that the discussion and results presented in this article reinvigorate interest in density matrix minimization methods.

Superoscillations Deliver Superspectroscopy.

In ordinary circumstances the highest frequency present in a wave is the highest frequency in its Fourier decomposition. It is however possible for there to be a spatial or temporal region where the wave locally oscillates at a still greater frequency in a phenomenon known as superoscillation. Superoscillations find application in wide range of disciplines, but at present their generation is based upon constructive approaches that are difficult to implement. Here, we address this, exploiting the fact that superoscillations are a product of destructive interference to produce a prescription for generating superoscillations from the superposition of arbitrary waveforms. As a first test of the technique, we use it to combine four quasisinusoidal THz waveforms to produce THz optical superoscillations for the first time. The ability to generate superoscillations in this manner has potential application in a wide range of fields, which we demonstrate with a method we term "superspectroscopy." This employs the generated superoscillations to obtain an observed enhancement of almost an order of magnitude in the spectroscopic sensitivity to materials whose resonance lies outside the range of the component waveform frequencies.

Optical Indistinguishability via Twinning Fields.

Here we introduce the concept of the twinning field-a driving electromagnetic pulse that induces an identical optical response from two distinct materials. We show that for a large class of pairs of generic many-body systems, a twinning field which renders the systems optically indistinguishable exists. The conditions under which this field exists are derived, and this analysis is supplemented by numerical calculations of twinning fields for both the 1D Fermi-Hubbard model, and tight-binding models of graphene and hexagonal boron nitride. The existence of twinning fields may lead to new research directions in nonlinear optics, materials science, and quantum technologies.

Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics.

A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-Bargmann-Michel-Telegdi equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy conserving, volume conserving, and second-order convergent. These properties are analyzed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long-time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane-wave field configuration.

Robust polarimetry via convex optimization.

We present mathematical methods, based on convex optimization, for correcting non-physical coherency matrices measured in polarimetry. We also develop the method for recovering the coherency matrices corresponding to the smallest and largest values of the degree of polarization given the experimental data and a specified tolerance. We use experimental non-physical results obtained with the standard polarimetry scheme and a commercial polarimeter to illustrate these methods. Our techniques are applied in post-processing, which complements other experimental methods for robust polarimetry.

Driven Imposters: Controlling Expectations in Many-Body Systems.

We present a framework for controlling the observables of a general correlated electron system driven by an incident laser field. The approach provides a prescription for the driving required to generate an arbitrary predetermined evolution for the expectation value of a chosen observable, together with a constraint on the maximum size of this expectation. To demonstrate this, we determine the laser fields required to exactly control the current in a Fermi-Hubbard system under a range of model parameters, fully controlling the nonlinear high-harmonic generation and optically observed electron dynamics in the system. This is achieved for both the uncorrelated metalliclike state and deep in the strongly correlated Mott insulating regime, flipping the optical responses of the two systems so as to mimic the other, creating "driven imposters." We also present a general framework for the control of other dynamical variables, opening a new route for the design of driven materials with customized properties.

Combining Lindblad Master Equation and Surface Hopping to Evolve Distributions of Quantum Particles.

Motivated by the need to study nonequilibrium evolutions of many-electron systems at the atomistic ab initio level, as they occur in modern devices and applications, we developed a quantum dynamics approach bridging master equations and surface hopping (SH). The Lindblad master equation (LME) allows us to propagate efficiently ensembles of particles, while SH provides nonperturbative evaluation of transition rates that evolve in time and depend explicitly on nuclear geometry. We implemented the LME-SH technique within real-time time-dependent density functional theory using global flux SH, and we demonstrated its efficiency and utility by modeling metallic films, in which charge-phonon dynamics was studied experimentally and showed an unexpectedly strong dependence on adhesion layers. The LME-SH approach provides a general framework for modeling efficiently quantum dynamics in a broad range of complex many-electron condensed-matter and nanoscale systems.

Uncomputability and complexity of quantum control.

In laboratory and numerical experiments, physical quantities are known with a finite precision and described by rational numbers. Based on this, we deduce that quantum control problems both for open and closed systems are in general not algorithmically solvable, i.e., there is no algorithm that can decide whether dynamics of an arbitrary quantum system can be manipulated by accessible external interactions (coherent or dissipative) such that a chosen target reaches a desired value. This conclusion holds even for the relaxed requirement of the target only approximately attaining the desired value. These findings do not preclude an algorithmic solvability for a particular class of quantum control problems. Moreover, any quantum control problem can be made algorithmically solvable if the set of accessible interactions (i.e., controls) is rich enough. To arrive at these results, we develop a technique based on establishing the equivalence between quantum control problems and Diophantine equations, which are polynomial equations with integer coefficients and integer unknowns. In addition to proving uncomputability, this technique allows to construct quantum control problems belonging to different complexity classes. In particular, an example of the control problem involving a two-mode coherent field is shown to be NP-hard, contradicting a widely held believe that two-body problems are easy.

Koopman wavefunctions and classical-quantum correlation dynamics.

Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect-the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. For example, the density matrix of the quantum subsystem is always positive definite. While the Liouville density of the classical subsystem is generally allowed to be unsigned, its sign is shown to be preserved in time for a specific infinite family of hybrid classical-quantum systems. The proposed description is illustrated and compared with previous theories using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

Entropy nonconservation and boundary conditions for Hamiltonian dynamical systems.

Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new dynamical phase associated with such a construction is identified. By choosing distributions not belonging to this class, we produce explicit examples of both free particles and harmonic systems evolving in a bounded phase-space in such a way that entropy is nonconserved. While these nonconserving states are classically forbidden, they may be interpreted as states of a quantum system tunneling through a potential barrier boundary. In this case, the allowed boundary conditions are the only distinction between classical and quantum systems. We show that the boundary conditions for a tunneling quantum system become the criteria for entropy preservation in the classical limit. These findings highlight how boundary effects drastically change the nature of a system.

Nonconservative Forces via Quantum Reservoir Engineering.

A systematic approach is given for engineering dissipative environments that steer quantum wave packets along desired trajectories. The methodology is demonstrated with several illustrative examples: environment-assisted tunneling, trapping, effective mass assignment, and pseudorelativistic behavior. Nonconservative stochastic forces do not inevitably lead to decoherence-we show that purity can be well preserved. These findings highlight the flexibility offered by nonequilibrium open quantum dynamics.

No Thermalization without Correlations.

The proof of the long-standing conjecture is presented that Markovian quantum master equations are at odds with quantum thermodynamics under conventional assumptions of fluctuation-dissipation theorems (implying a translation invariant dissipation). Specifically, except for identified systems, persistent system-bath correlations of at least one kind, spatial or temporal, are obligatory for thermalization. A systematic procedure is proposed to construct translation invariant bath models producing steady states that well approximate thermal states. A quantum optical scheme for the laboratory assessment of the developed procedure is outlined.

Analytic Solutions to Coherent Control of the Dirac Equation.

A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show how to achieve dispersionless rotation and translation of wave packets. Additionally, this formalism can handle control interactions beyond electromagnetic. This work reveals unexpected flexibility of the Dirac equation for control applications, which may open new prospects for quantum technologies.

How to Make Distinct Dynamical Systems Appear Spectrally Identical.

We show that a laser pulse can always be found that induces a desired optical response from an arbitrary dynamical system. As illustrations, driving fields are computed to induce the same optical response from a variety of distinct systems (open and closed, quantum and classical). As a result, the observed induced dipolar spectra without detailed information on the driving field are not sufficient to characterize atomic and molecular systems. The formulation may also be applied to design materials with specified optical characteristics. These findings reveal unexplored flexibilities of nonlinear optics.

Erratum: Analytic Solutions to Coherent Control of the Dirac Equation [Phys. Rev. Lett. 119, 173203 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.173203.

Efficient computations of quantum canonical Gibbs state in phase space.

The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation.

Photonic reagents for concentration measurement of flu-orescent proteins with overlapping spectra.

By exploiting photonic reagents (i.e., coherent control by shaped laser pulses), we employ Optimal Dynamic Discrimination (ODD) as a novel means for quantitatively characterizing mixtures of fluorescent proteins with a large spectral overlap. To illustrate ODD, we simultaneously measured concentrations of in vitro mixtures of Enhanced Blue Fluorescent Protein (EBFP) and Enhanced Cyan Fluorescent Protein (ECFP). Building on this foundational study, the ultimate goal is to exploit the capabilities of ODD for parallel monitoring of genetic and protein circuits by suppressing the spectral cross-talk among multiple fluorescent reporters.

Wigner-Lindblad Equations for Quantum Friction.

Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.

Operational dynamic modeling transcending quantum and classical mechanics.

We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.