A $\mathcal{PT}$-symmetric Bose-Einstein condensate can theoretically be described using a complex optical potential, however, the experimental realization of such an optical potential describing the coherent incoupling and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum-mechanical realization of a $\mathcal{PT}$-symmetric system, where the $\mathcal{PT}$-symmetric currents are implemented by an accelerating Bose-Einstein condensate in a titled optical lattice. A defect consisting of two wells at the same energy level then acts as a $\mathcal{PT}$-symmetric double well if the tilt in the energy offsets of all further wells in the lattice is varied in time. We map the time dependence of the amplitudes of a frozen Gaussian variational ansatz to a matrix model and increase the system size step by step starting with a six-well setup. In terms of this simple matrix model, we derive conditions under which two wells of the Hermitian multiwell system behave exactly as the two wells of the $\mathcal{PT}$-symmetric system.

Recent breakthroughs in the experimental manipulation of strongly interacting atomic Rydberg gases in lattice potentials have opened an avenue for the study of many-body phenomena. Considerable efforts are currently being undertaken to achieve clean experimental settings that show a minimal amount of noise and disorder and are close to zero temperature. A complementary direction investigates the interplay between coherent and dissipative processes. Recent experiments have revealed a glimpse into the emergence of a rich nonequilibrium behavior stemming from the competition of laser excitation, strong interactions, and radiative decay of Rydberg atoms. The aim of the present theoretical work is to show that local incoherent loss and gain of atoms can in fact be the source of interesting out-of-equilibrium dynamics. This perspective opens up paths for the exploration of nonequilibrium critical phenomena and, more generally, phase transitions, some of which so far have been rather difficult to study. To demonstrate the richness of the encountered dynamical behavior we consider here three examples. The first two feature local atom loss and gain together with an incoherent excitation of Rydberg states. In this setting either a continuous or a discontinuous phase transition emerges with the former being reminiscent of genuine nonequilibrium transitions of stochastic processes with multiple absorbing states. The third example considers the regime of coherent laser excitation. Here the many-body dynamics is dominated by an equilibrium transition of the “model A” universality class.

The lifetimes of the lower-lying vibrational states of ultra-long-range strontium Rydberg molecules comprising one ground-state $5s^2$ ${}^1{S}_0$ atom and one Rydberg atom in the $5s38s{}^3{S}_1$ state are reported. The molecules are created in an ultracold gas held in an optical dipole trap and their numbers determined using field ionization, the product electrons being detected by a microchannel plate. The measurements show that, in marked contrast to earlier measurements involving rubidium Rydberg molecules, the lifetimes of the low-lying molecular vibrational states are very similar to those of the parent Rydberg atoms. This results because the strong $p$-wave resonance in low-energy electron-rubidium scattering, which strongly influences the rubidium molecular lifetimes, is not present for strontium. The absence of this resonance offers advantages for experiments involving strontium Rydberg atoms as impurities in quantum gases and for testing of theories of molecular formation and decay.

We analyze the operation of a sensor based on atom interferometry, which can achieve supraclassical sensitivity by exploiting quantum correlations in mixed states of many qubits. The interferometer is based on quantum gates which use coherently controlled Rydberg interactions between a single atom (which acts as a control qubit) and an atomic ensemble (which provides register qubits). In principle, our scheme can achieve precision scaling with the size of the ensemble—which can extend to large numbers of atoms—while using only single-qubit operations on the control and bulk operations on the ensemble. We investigate realistic implementation of the interferometer, and our main aim is to develop an approach to quantum metrology that can achieve quantum-enhanced measurement precision by exploiting coherent operations on large impure quantum states. We propose an experiment to demonstrate the enhanced sensitivity of the protocol and to investigate a transition from classical to supraclassical sensitivity which occurs when using highly mixed probe states.

We present absolute-frequency measurements for the transitions from the $6s_{1/2}$ ground state of ${}^{133}\mathrm{Cs}$ to $n{p}_{1/2}$ and $n{p}_{3/2}$ Rydberg states. The transition frequencies are determined by one-photon UV spectroscopy in ultracold samples of Cs atoms using a narrow-band laser system referenced to a frequency comb. From a global fit of the ionization energy $E_{\mathrm{I}}$ and the quantum defects of the two series we determine an improved value of $E_{\mathrm{I}}/hc=31406.4677325\left(14\right){\mathrm{cm}}^{-1}$ for the ionization energy of Cs with a relative uncertainty of $5\times {10}^{-11}$. We also report improved values for the quantum defects of the $n{p}_{1/2}, n{p}_{3/2}, n{s}_{1/2}$, and $n{d}_{5/2}$ series.

We propose to use a nonlinear resonator for projective readout, classical memory, and feedback for a superconducting qubit. Keeping the classical controller at cryogenic temperatures sidesteps many of the inefficiencies inherent in two-way communication between temperature stages in typical systems with room-temperature controllers, and avoids increasing the cryogenic heat load. This controller may find a broad range of uses in multiqubit systems, but here we analyze two specific demonstrative cases in single qubit control. In the first case, the nonlinear controller is used to initialize the qubit in a definite eigenstate. And in the second case, the qubit's state is read into the controller's classical memory and used to reinstate the measured state after the qubit has decayed. We analyze the properties of this system and we show simulations of the time evolution for the full system dynamics.

Entanglement is the resource to overcome the restriction of operations to local operations assisted by classical communication (LOCC). The maximally entangled set (MES) of states is the minimal set of $n$-partite pure states with the property that any truly $n$-partite entangled pure state can be obtained deterministically via LOCC from some state in this set. Hence, this set contains the most useful states for applications. In this work, we characterize the MES for generic three-qutrit states. Moreover, we analyze which generic three-qutrit states are reachable (and convertible) under LOCC transformations. To this end, we study reachability via separable operations (SEP), a class of operations that is strictly larger than LOCC. Interestingly, we identify a family of pure states that can be obtained deterministically via SEP but not via LOCC. This gives an affirmative answer to the question of whether there is a difference between SEP and LOCC for transformations among pure states.

We present an experimental realization of a quantum digital signature protocol which, together with a standard quantum key distribution link, increases transmission distance to kilometer ranges, three orders of magnitude larger than in previous realizations. The bit rate is also significantly increased compared with previous quantum signature demonstrations. This work illustrates that quantum digital signatures can be realized with optical components similar to those used for quantum key distribution and could be implemented in existing quantum optical fiber networks.

Photoelectron spectra and photoelectron angular distributions obtained in photoionization reveal important information on, e.g., charge transfer or hole coherence in the parent ion. Here we show that optimal control of the underlying quantum dynamics can be used to enhance desired features in the photoelectron spectra and angular distributions. To this end, we combine Krotov's method for optimal control theory with the time-dependent configuration interaction singles formalism and a splitting approach to calculate photoelectron spectra and angular distributions. The optimization target can account for specific desired properties in the photoelectron angular distribution alone, in the photoelectron spectrum, or in both. We demonstrate the method for hydrogen and then apply it to argon under strong XUV radiation, maximizing the difference of emission into the upper and lower hemispheres, in order to realize directed electron emission in the XUV regime.

In quantum optimal control theory the success of an optimization algorithm is highly influenced by how the figure of merit to be optimized behaves as a function of the control field, i.e., by the control landscape. Constraints on the control field introduce local minima in the landscape—false traps—which might prevent an efficient solution of the optimal control problem. Rabitz et al. [Science 303, 1998 (2004)] showed that local minima occur only rarely for unconstrained optimization. Here, we extend this result to the case of bandwidth-limited control pulses showing that in this case one can eliminate the false traps arising from the constraint. Based on this theoretical understanding, we modify the chopped-random-basis (CRAB) optimal control algorithm and show that this development exploits the advantages of both (unconstrained) gradient algorithms and of truncated basis methods, allowing one to always follow the gradient of the unconstrained landscape by bandwidth-limited control functions. We study the effects of additional constraints and show that for reasonable constraints the convergence properties are still maintained. Finally, we numerically show that this approach saturates the theoretical bound on the minimal bandwidth of the control needed to optimally drive the system.

In this work, we study the formation and dynamics of polarons in a system with a few impurities in a lattice immersed in a Bose-Einstein condensate (BEC). This system has been experimentally realized using ultracold atoms and optical lattices. Here, we consider a two-band model for the impurity atoms, along with a Bogoliubov approximation for the BEC, with phonons coupled to impurities via both intraband and interband transitions. We decouple this Fröhlich-type term by an extended two-band Lang-Firsov polaron transformation using a variational method. The new effective Hamiltonian with two (polaron) bands differs from the original Hamiltonian by modified coherent transport, polaron energy shifts, and induced long-range interaction. A Lindblad master-equation approach is used to take into account residual incoherent coupling between polaron and bath. This polaronic treatment yields a renormalized interband relaxation rate compared to Fermi's golden rule. For a strongly coupled two-band Fröhlich Hamiltonian, the polaron is tightly dressed in each band and can not tunnel between them, leading to an interband self-trapping effect.

Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality witnesses can be expressed as a sum $S$ of $n$ probabilities, and the independence number $\alpha$ and the Tsirelson-like number $\vartheta$ of the corresponding exclusivity graph are, respectively, the maximum of $S$ for noncontextual theories and for the theory under consideration. A theory allows for absolute maximal contextuality if it has scenarios in which $\vartheta /\alpha$ approaches $n$. Here we show that quantum theory allows for absolute maximal contextuality despite what is suggested by the examination of the quantum violations of Bell and noncontextuality inequalities considered in the past. Our proof is not constructive and does not single out explicit scenarios. Nevertheless, we identify scenarios in which quantum theory allows for almost-absolute-maximal contextuality.

In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NLUBB) whose inward Hänkel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines the NLUBB attractor is given. Steady or unsteady propagation depends on whether the attracting NLUBB has a small, exponentially growing, unstable mode. In the case of unsteady propagation, periodic, quasiperiodic, or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.

One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground-state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to determine its phase diagram and ground-state properties on a quantum computer. In particular, we discuss strategies for efficiently determining and preparing the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prepare arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms, each time step in the evolution can be performed with just $O\left(N\right)$ gates and $O(logN)$ circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, in both the time and the frequency domains. We further present efficient nondestructive approaches to measurement that avoid the need to reprepare the ground state after each measurement and that quadratically reduce the measurement error.

We demonstrate fluorescence microscopy of individual fermionic potassium atoms in a 527-nm-period optical lattice. Using electromagnetically induced transparency cooling on the 770.1-nm $D_1$ transition of ${}^{40}\mathrm{K}$, we find that atoms remain at individual sites of a 0.2-mK-deep lattice, with a $1/e$ pinning lifetime of $67\left(9\right)\mathrm{s}$, while scattering $\sim {10}^3$ photons per second. The plane to be imaged is isolated using microwave spectroscopy in a magnetic-field gradient, and can be chosen at any depth within the three-dimensional lattice. With a similar protocol, we also demonstrate patterned selection within a single lattice plane. High-resolution images are acquired using a microscope objective with 0.8 numerical aperture, from which we determine the occupation of lattice sites in the imaging plane with 94(2)% fidelity per atom. Imaging with single-atom sensitivity and addressing with single-site accuracy are key steps towards the search for unconventional superfluidity of fermions in optical lattices, the initialization and characterization of transport and nonequilibrium dynamics, and the observation of magnetic domains.

We present results of high-precision calculations for a boron atom's properties using wave functions expanded in the explicitly correlated Gaussian basis. We demonstrate that the well-optimized 8192 basis functions enable a determination of energy levels, ionization potential, and fine and hyperfine splittings in atomic transitions with nearly parts per million precision. The results open a window to a spectroscopic determination of nuclear properties of boron including the charge radius of the proton halo in the ${}^8\mathrm{B}$ nucleus.

Quantum entanglement may provide a huge boost in the precision of parameter estimation. However, quantum metrology seems to be extremely sensitive to noise in the probe state. There is an important still open question: What type of entanglement is useful as a resource in quantum metrology? Here we raise this question in relation to entanglement distillation. We provide a counterintuitive example of a family of bound entangled states which can be used in quantum enhanced metrology with the precision advantage approaching the Heisenberg limit. This shows that so-called distillability is not necessary for quantum advantage in metrology. Surprisingly, entanglement of the applied states is very weak, which is reflected by the lack of the so-called unlockability property. Moreover we find instances where quantum Fisher information reports the presence of entanglement where a well-known class of nonlinear entanglement witnesses (stronger than multisetting correlation Bell inequalities) does not. We have thus provided strong evidence that quantum metrology can be treated as additional operational face of multipartite entanglement, independent of two other basic operational features used in quantum information theory: nonlocality and distillability.

Quantum key distribution (QKD) has the potential to improve communications security by offering cryptographic keys whose security relies on the fundamental properties of quantum physics. The use of a trusted quantum receiver on an orbiting satellite is the most practical near-term solution to the challenge of achieving long-distance (global-scale) QKD, currently limited to a few hundred kilometers on the ground. This scenario presents unique challenges, such as high photon losses and restricted classical data transmission and processing power due to the limitations of a typical satellite platform. Here we demonstrate the feasibility of such a system by implementing a QKD protocol, with optical transmission and full post-processing, in the high-loss regime using minimized computing hardware at the receiver. Employing weak coherent pulses with decoy states, we demonstrate the production of secure key bits at up to 56.5 dB of photon loss. We further illustrate the feasibility of a satellite uplink by generating a secure key while experimentally emulating the varying losses predicted for realistic low-Earth-orbit satellite passes at 600 km altitude. With a 76 MHz source and including finite-size analysis, we extract 3374 bits of a secure key from the best pass. We also illustrate the potential benefit of combining multiple passes together: while one suboptimal “upper-quartile” pass produces no finite-sized key with our source, the combination of three such passes allows us to extract 165 bits of a secure key. Alternatively, we find that by increasing the signal rate to 300 MHz it would be possible to extract 21 570 bits of a secure finite-sized key in just a single upper-quartile pass.

We study the case of $\mathcal{PT}$-symmetric perturbations of Hermitian Hamiltonians with degenerate eigenvalues using the example of a triple-well system. The degeneracy complicates the question of whether or not a stationary current through such a system can be established, i.e., whether or not the $\mathcal{PT}$-symmetric states are stable. It is shown that this is only the case for perturbations that do not couple to any of the degenerate states. The physical explanation for the inhibition of stable currents is discussed. However, introducing an on-site interaction restores the capability to support stable currents.

We investigate the localization properties of atoms moving in a three-dimensional optical lattice in the presence of a disorder potential having the same probability distribution $P\left(V\right)$ as laser speckles, and a spatial correlation length much shorter than the lattice spacing. We find that the disorder-averaged (single-particle) Green's function, calculated via the coherent-potential approximation, is in very good agreement with exact numerics. Using the transfer-matrix method, we compute the phase diagram in the energy-disorder plane and show that its peculiar shape can be understood from the self-consistent theory of localization. In particular, we recover the large asymmetry in the position of the mobility edge for blue and red speckles, which was recently observed numerically for spatially correlated speckle potentials.