We show that pronounced modulations in spin and charge densities can be induced by the insertion of a single hole in an otherwise half-filled two-leg Hubbard ladder. Accompanied with these modulations is a loosely bound structure of the doped charge with a spin-1/2, in contrast to the tightly bound case where such modulations are absent. These behaviors are caused by the interference of the Berry phases associated with a string of flipped spins (or “phase strings”) left behind as a hole travels through a spin bath with a short-range antiferromagnetic order. The key role of the phase strings is also reflected in how the system responds to increasing spin polarization and the on-site repulsion, addition of a second hole, and increasing asymmetry between intra- and interchain hopping. Remarkably, all these properties persist down to ladders as short as $\sim 10$ sites, as the smoking gun of the phase-string effect. They can therefore be studied in cold-atom experiments using the recently developed fermion microscope.

We present a theoretical and experimental study of the generation of photon pairs through the process of spontaneous four-wave mixing (SFWM) in a few-mode, birefringent fiber. Under these conditions, multiple SFWM processes are in fact possible, each associated with a different combination of transverse modes for the four waves involved. We show that in the weakly guiding regime, for which the propagation modes may be well approximated by linearly polarized modes, the departure from circular symmetry due to the fiber birefringence translates into conservation rules, which retain elements from azimuthal and rectangular symmetries: both OAM and parity must be conserved for a process to be viable. We have implemented a SFWM source based on a bowtie birefringent fiber, and have measured for a collection of pump wavelengths the SFWM spectra of each of the signal and idler photons in coincidence with its partner photon. We have used this information, together with knowledge of the transverse modes into which the signal and idler photons are emitted, as input for a genetic algorithm, which accomplishes two tasks: (i) the identification of the particular SFWM processes that are present in the source, and (ii) the characterization of the fiber used.

We investigate theoretically the light amplification by stimulated emission of radiation (laser) in the ultrastrong light-matter interaction regime under the two-level and single-mode approximations. The conventional picture of the laser is broken under the ultrastrong interaction. Instead, we must explicitly discuss the dynamics of the electric field and of the magnetic one distinctively, which make the “laser” qualitatively different from the conventional laser. We found that the laser generally accompanies odd-order harmonics of the electromagnetic fields both inside and outside the cavity and a synchronization with an oscillation of atomic population. A bistability is also demonstrated. However, since our model is quite simplified, we got quantitatively different results from the Hamiltonians in the velocity and length forms of the light-matter interaction, while the appearance of the multiple harmonics and the bistability is qualitatively reliable.

We study the fluorescence spectrum from a two-level system with a controllable energy separation modulated by the longitudinal field and excited by the transversal field. Combining the rotating-wave approximation and the Floquet theory, we derive a formal solution to the Bloch equations in the presence of both longitudinal and transversal driving fields and numerically evaluate the fluorescence spectrum. Exotic spectral features associated with the added longitudinal driving are found to be dramatically different from the standard Mollow triplet with a multipeak structure. The spectrum may be experimentally realized in the context of artificial atoms in a superconducing circuit.

Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers sharing some configuration of many independent physical systems. Here, we show how to construct Bell-type inequalities for correlations arising in any tree-structured network, i.e., networks without cycles. This is achieved by an iteration procedure that in each step allows one to add a branch to the tree-structured network and construct a corresponding Bell-type inequality. We explore our inequalities in several examples, in all of which we demonstrate strong violations from quantum theory.

We show the existence of periodic exploding dissipative solitons. These nonchaotic explosions appear when higher-order nonlinear and dispersive effects are added to the complex cubic-quintic Ginzburg-Landau equation modeling fiber soliton lasers. This counterintuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations leading to chaos (chaotic explosions).

We demonstrate how quantum optimal control can be used to enhance quantum resources for bipartite one-way protocols, specifically Einstein-Podolsky-Rosen steering with qubit measurements. Steering is relevant for one-sided device-independent key distribution, the realistic implementations of which necessitate the study of noisy scenarios. So far, mainly the case of imperfect detection efficiency has been considered; here we look at the effect of dynamical noise responsible for decoherence and dissipation. In order to set up the optimization, we map the steering problem into the equivalent joint measurability problem and employ quantum resource-theoretic robustness monotones from that context. The advantage is that incompatibility (hence steerability) with arbitrary pairs of noisy qubit measurements has been completely characterized through an analytical expression, which can be turned into a computable cost function with exact gradient. Furthermore, dynamical loss of incompatibility has recently been illustrated by using these monotones. We demonstrate resource control numerically by using a special gradient-based software showing, in particular, the advantage over naive control with cost function chosen as a fidelity in relation to a specific target. We subsequently illustrate the complexity of the control landscapes with a simplified two-variable scheme. The results contribute to the theoretical understanding of the limitations in realistic implementations of quantum information protocols, also paving the way to practical use of the rather abstract quantum resource theories.

We investigate the spin-$1/2$ relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to ${\alpha }^{n}G$, where $\alpha$ is the fine-structure constant and $G$ is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

We study the spectrum of the hydrogen atom in Snyder space in a semiclassical approximation based on a generalization of the Born-Sommerfeld quantization rule. While the corrections to the standard quantum mechanical spectrum arise at first order in the Snyder parameter for the $l=0$ states, they are of second order for $l\ne 0$. This can be understood as due to the different topology of the regions of integration in phase space.

We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate quantum adiabatic optimization algorithms during a quantum tunneling process. Specifically we look at symmetric cost functions defined over $n$ bits with a single potential barrier that a successful quantum adiabatic optimization algorithm will have to tunnel through. The height and width of this barrier depend on $n$, and by tuning these dependencies, we can make the optimization algorithm succeed or fail in polynomial time. In this article we compare the strength of quantum adiabatic tunneling with that of path-integral quantum Monte Carlo methods. We find numerical evidence that quantum Monte Carlo algorithms will succeed in the same regimes where quantum adiabatic optimization succeeds.

We examine the effect of network heterogeneity on the performance of quantum search algorithms. To this end, we study quantum search on a tree for the oracle Hamiltonian formulation employed by continuous-time quantum walks. We use analytical and numerical arguments to show that the exponent of the asymptotic running time $\sim N^{\beta }$ changes uniformly from $\beta =0.5$ to $\beta =1$ as the searched-for site is moved from the root of the tree towards the leaves. These results imply that the time complexity of the quantum search algorithm on a balanced tree is closely correlated with certain path-based centrality measures of the searched-for site.

We study theoretically ultracold collisions in quasi-one-dimensional optical traps for bosonic and fermionic reactive molecules in the presence of a periodic potential along the trap axis. Elastic, reactive, and umklapp processes due to nonconservation of the center-of-mass motion are investigated for parameters of relevant experimental interest. The model naturally keeps into account the effect of excited energy bands and is particularly suited for being adapted to rigorous close-coupled calculations. Our formalism shows that a correct derivation of the parameters in tight-binding effective models must include the strong momentum dependence of the coupling constant we predict even for deep lattices.

We investigate the evolution of extreme ultraviolet (XUV) spectral line shapes in an optically thick helium gas under near-infrared (IR) perturbation. In our experimental and theoretical work, we systematically vary the IR intensity, time-delay, gas density, and IR polarization parameters to study line-shape modifications induced by collective interactions in a regime beyond the single-atom response of a thin, dilute gas. In both experiment and theory, we find that specific features in the frequency-domain absorption profile, and their evolution with propagation distance, can be attributed to the interplay between resonant attosecond pulse propagation and IR-induced phase shifts. Our calculations show that this interplay also manifests itself in the time domain, with the IR pulse influencing the reshaping of the XUV pulse propagating in the resonant medium.

In two dimensions, the Fourier transform of the interaction between two point dipoles has a term which grows linearly in the modulus $\left|\mathit{q}\right|$ of the momentum. As a consequence, in second-order perturbation theory, the self-energy of two-dimensional dipolar fermions is ultraviolet divergent. We show that for electric dipoles, this divergence can be avoided if one takes into account that physical dipoles consist of two opposite charges which are separated by a finite distance. Using this regularization, we calculate the self-energy, the renormalized chemical potential, and the renormalized Fermi surface of dipolar fermions in two dimensions in second-order perturbation theory. We find that in the Fermi liquid phase, the second-order corrections weaken first-order effects.

Motivated by recent experiments, we investigate a single ${}^{133}\text{Cs}$ impurity in the center of a trapped ${}^{87}\text{Rb}$ Bose-Einstein condensate (BEC). Within a zero-temperature mean-field description we provide a one-dimensional physical intuitive model which involves two coupled differential equations for the condensate and the impurity wave function, which we solve numerically. With this we determine within the equilibrium phase diagram spanned by the intra- and interspecies coupling strength whether the impurity is localized at the trap center or expelled to the condensate border. In the former case we find that the impurity induces a bump or dip on the condensate for an attractive or a repulsive Rb-Cs interaction strength, respectively. Conversely, the condensate environment leads to an effective mass of the impurity which increases quadratically for small interspecies interaction strength. Afterwards, we investigate how the impurity imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the impurity-induced bump in the condensate wave function starts decaying marginally, whereas the dip decays with a characteristic time scale which decreases with increasing repulsive impurity-BEC interaction strength. Second, once the attractive or repulsive interspecies coupling constant is switched off, we find that white-shock waves or bisolitons emerge which both oscillate within the harmonic confinement with a characteristic frequency.

The dynamics of skyrmions in a two-component Bose-Einstein condensate is numerically investigated in the mean-field theory. When two skyrmions collide with each other, they are first united and then scattered into various states. For head-on collisions, skyrmions with unit winding number are scattered. The collision dynamics with an impact parameter are shown to depend on the relative phase. These dynamic processes are characterized by integer winding numbers.

We have constructed an asymmetric matter-wave beam splitter and a ring potential on an atom chip with Bose-Einstein condensates using radio-frequency dressing. By applying rf field parallel to the quantization axis in the vicinity of the static trap minima added to perpendicular rf fields, versatile controllability on the asymmetry of rf-dressed potentials is realized. Asymmetry of the rf-induced double well is controlled over a wide range without discernible displacement of each well. Formation of an isotropic ring potential on an atom chip is achieved by compensating the gradient due to gravity and inhomogeneous coupling strength. In addition, position and rotation velocity of a BEC along the ring geometry are controlled by the relative phase and the frequency difference between the rf fields, respectively.

A general theory of sensors based on the detection of splittings of resonant frequencies or energy levels operating at so-called exceptional points is presented. Exploiting the complex-square-root topology near such non-Hermitian degeneracies has a great potential for enhanced sensitivity. Passive and active systems are discussed. The theory is specified for whispering-gallery microcavity sensors for particle detection. As example, a microdisk with two holes is studied numerically. The theory and numerical simulations demonstrate a sevenfold enhancement of the sensitivity.