We prepare and study a two-component Mott insulator of bosonic atoms with two particles per site. The mapping of this system to a magnetic spin model and the subsequent study of its quantum phases require a detailed knowledge of the interaction strengths of the two components. In this work we use radio-frequency transitions and an on-site interaction blockade for precise empirical determination of the interaction strengths of different combinations of hyperfine states on a single lattice site. We create a map of the interactions of the two lowest hyperfine states of ${}^7\mathrm{Li}$ as a function of magnetic field, including measurements of several Feshbach resonances with exceptional sensitivity, and we identify promising regions for the realization of magnetic spin models.

Optical quantum states defined in temporal modes, especially non-Gaussian states, such as photon-number states, play an important role in quantum computing schemes. In general, the temporal mode structures of these states are characterized by one or more complex functions called temporal mode functions (TMFs). Although we can calculate the TMF theoretically in some cases, experimental estimation of a TMF is more advantageous to utilize the states with high purity. In this paper, we propose a method to estimate complex TMFs. This method can be applied not only to arbitrary single temporal mode non-Gaussian states, but also to two temporal mode states containing two photons. This method is implemented by continuous-wave dual homodyne measurement and does not need prior information of the target states nor state reconstruction procedure. We demonstrate this method by analyzing several experimentally created non-Gaussian states.

We use extensive numerical simulations based on matrix product state methods to study the quantum dynamics of spin chains with strong on-site disorder and power-law decaying ($1/r^{\alpha }$) interactions. We focus on two spin-$1/2$ Hamiltonians featuring power-law interactions, Heisenberg and $XY$, and characterize their corresponding long-time dynamics using three distinct diagnostics: decay of a staggered magnetization pattern $I\left(t\right)$, growth of entanglement entropy $S\left(t\right)$, and growth of quantum Fisher information $F_Q\left(t\right).$ For sufficiently rapidly decaying interactions $\alpha >{\alpha }_c$ we find a many-body localized phase, in which $I\left(t\right)$ saturates to a nonzero value, entanglement entropy grows as $S\left(t\right)\propto t^{1/\alpha }$, and Fisher information grows logarithmically. Importantly, entanglement entropy and Fisher information do not scale the same way (unlike short-range interacting models). The critical power ${\alpha }_c$ is smaller for the $XY$ model than for the Heisenberg model.

A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. In contrast to typical discussions of BEC, our system is better treated with a controlled chemical potential rather than a controlled particle number, and is subject to energy-dependent loss. Here, we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline-earth atoms) inside a Fabry-Pérot cavity.

The learning-with-errors (LWE) problem is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of postquantum cryptography. In this work, we study the quantum sample complexity of learning with errors and show that there exists an efficient quantum learning algorithm (with polynomial sample and time complexity) for the learning-with-errors problem where the error distribution is the one used in cryptography. While our quantum learning algorithm does not break the LWE-based encryption schemes proposed in the cryptography literature, it does have some interesting implications for cryptography: if a quantum adversary has access to a particular superposition of quantum states, a LWE-based encryption scheme becomes insecure. In particular, if a quantum sample state could be created from classical samples, then it would be possible to break LWE-based schemes using our learning algorithm. Finally, we extend our results and show quantum learning algorithms for three related problems: learning parity with noise, learning with rounding, and short integer solution.

We derive an extension of the quantum regression theorem to calculate out-of-time-order correlation functions in Markovian open quantum systems. While so far mostly being applied in the analysis of many-body physics, we demonstrate that out-of-time-order correlation functions appear naturally in optical detection schemes with interferometric delay lines, and we apply our extended quantum regression theorem to calculate the nontrivial photon counting fluctuations in split and recombined signals from a quantum light source.

We show how to create quantum squeezed states of magnons and phonons in a cavity magnomechanical system. The magnons are embodied by a collective motion of a large number of spins in a macroscopic ferrimagnet, and couple to cavity microwave photons and phonons (vibrational modes of the ferrimagnet) via the magnetic dipole interaction and magnetostrictive interaction, respectively. The cavity is driven by a weak squeezed vacuum field generated by a flux-driven Josephson parametric amplifier, which is essential to get squeezed states of the magnons and phonons. We show that the magnons can be prepared in a squeezed state via the cavity-magnon beam-splitter interaction, and by further driving the magnon mode with a strong red-detuned microwave field, the phonons are squeezed. We show optimal parameter regimes for obtaining large squeezing of the magnons and phonons, which are robust against temperature and could be realized with experimentally reachable parameters.

We study the early-time dynamics of a degenerate Bose gas after a sudden quench of the interaction strength, starting from a weakly interacting gas. By making use of a time-dependent generalization of the Nozières-Saint-James variational formalism, we describe the crossover of the early-time dynamics from shallow to deep interaction quenches. We analyze the coherent oscillations that characterize both the density of excited states and the Tan's contact as a function of the final scattering length. For shallow quenches, the oscillatory behavior is negligible and the dynamics is universally governed by the healing length and the mean-field interaction energy. By increasing the final scattering length to intermediate values, we reveal a universal regime where the period of the coherent atom-molecule oscillations is set by the molecule binding energy. For the largest scattering lengths we can numerically simulate in the unitary regime, we find a universal scaling behavior of the typical growth time of the momentum distribution in agreement with recent experimental observations [C. Eigen et al., Nature 563, 221 (2018)].

Angularly resolved two-photon single ionization yields of helium resulting after the interaction with an ultrashort XUV pulse are obtained by numerically solving the full dimension time-dependent Schrödinger equation. The angular distributions reveal the underlying dominant mechanism, which depends on the effective photon energy absorbed and the pulse parameters. We specifically explore the contributions of radial and angular electron correlation terms. A single active electron picture is a qualitatively valid approach for the lowest photon energies, even in the above-threshold ionization region. Nonetheless, angular correlation plays a detectable role in the low-energy region and a major role at higher energies when autoionizing states are populated. As the photon energy increases, sequential ionization-excitation dominates; therefore, the resulting probability distributions are explained as the result of two active uncorrelated electrons. This uncorrelated picture fails again for photon energies above ionization potential of the ion.

The indistinguishability of nonorthogonal pure states lies at the heart of quantum information processing. Although the indistinguishability reflects the impossibility of measuring complementary physical quantities by a single measurement, we demonstrate that the distinguishability can be perfectly retrieved simply with the help of posterior classical partial information. We demonstrate this by showing an ensemble of nonorthogonal pure states such that a state randomly sampled from the ensemble can be perfectly identified by a single measurement with the help of postprocessing of the measurement outcomes and additional partial information about the sampled state, i.e., the label of the subensemble from which the state is sampled. When an ensemble consists of two subensembles, we show that the perfect distinguishability of the ensemble with the help of postprocessing can be restated as a matrix-decomposition problem. Furthermore, we give the analytical solution for the problem when both subensembles consist of two states.

We report on the use of $4.7\text{−}\mu \mathrm{m}$-diameter, optically levitated, charged microspheres to image the three-dimensional force field produced by charge distributions on an Au-coated, microfabricated Si beam in vacuum. An upward-propagating, single-beam optical trap, combined with an interferometric imaging technique, provides optimal access to the microspheres for microscopy. In this demonstration, the Au-coated surface of the Si beam can be brought as close as $\sim 10\mu \mathrm{m}$ from the center of the microsphere while forces are simultaneously measured along all three orthogonal axes, fully mapping the vector force field over a total volume of $\sim {10}^6\mu {\mathrm{m}}^3$. We report a force sensitivity of $(2.5\pm 1.0)\times {10}^{-17}\mathrm{N}/\sqrt{\mathrm{Hz}}$, in each of the three degrees of freedom, with a linear response to up to $\sim {10}^{-13}\mathrm{N}$. While we discuss the case of mapping static electric fields using charged microspheres, it is expected that the technique can be extended to other force fields, using microspheres with different properties.

We report on a scheme to cool and compress trapped clouds of highly magnetic ${}^{52}\mathrm{Cr}$ atoms. This scheme combines sequences of gray molasses, which freeze the velocity distribution, and free evolutions in the (close to) harmonic trap, which periodically exchange the spatial and velocity degrees of freedom. Taken together, the successive gray molasses pulses cool all external degrees of freedom, which leads to an increase of the phase-space density (PSD) by a factor of $\approx 250$, allowing to reach a high final PSD of $\approx 1.7\times {10}^{-3}$. These experiments are performed within an optical dipole trap, in which gray molasses works as well as it does in free space. The obtained samples are then an ideal starting point for the evaporation stage aiming at the quantum regime.

We experimentally and theoretically investigate the lowest-lying axial excitation of an atomic Bose-Einstein condensate in a cylindrical box trap. By tuning the atomic density, we observe how the nature of the mode changes from a single-particle excitation (in the low-density limit) to a sound wave (in the high-density limit). Throughout this crossover the measured mode frequency agrees with Bogoliubov theory. Using approximate low-energy models we show that the evolution of the mode frequency is directly related to the interaction-induced shape changes of the condensate and the excitation. Finally, if we create a large-amplitude excitation, and then let the system evolve freely, we observe that the mode amplitude decays nonexponentially in time; this nonlinear behavior is indicative of interactions between the elementary excitations, but remains to be quantitatively understood.

There have been concerted efforts in recent years to realize the next generation of clocks using alkaline earth atoms in an optical lattice. Assuming that the atoms are independent, such a clock would benefit from a $\sqrt{N}$ enhancement in its stability, associated with the improved signal-to-noise ratio of a large atom number $N$. An interesting question, however, regards what type of atomic interactions might affect the clock dynamics and whether these interactions are deleterious or could even be beneficial. In this work, we investigate the effect of dipole-dipole interactions, in which atoms excited during the clock protocol emit and reabsorb photons. Taking a simple system consisting of a one-dimensional atomic array, we find that dipole-dipole interactions in fact result in an open quantum system exhibiting critical dynamics, as a set of collective excitations acquires a decay rate approaching zero in the thermodynamic limit due to subradiance. A first consequence is that the decay of atomic excited population at long times exhibits a slow power-law behavior, instead of the exponential expected for noninteracting atoms. We also find that excitations among the atoms exhibit fermionic spatial correlations at long times, due to the microscopic properties of the multiexcitation subradiant states. Interestingly, these properties cannot be captured by mean-field dynamics, suggesting the strongly interacting nature of this system. We finally characterize the time-dependent frequency shift in the atomic frequency measurement and find that it is dominated by the interaction energy of subradiant states at long times. Furthermore, we show that the decay of the clock signal displays at long times a nonexponential behavior, which might be useful to improve the uncertainty limit with which the atomic frequency can be resolved. We attribute the lack of robust power-law dynamics for the clock signal to an effective many-body dephasing caused by purely coherent interactions.

Optical cavities are widely used to enhance the interaction between atoms and light. Typical designs using a geometrically symmetric structure in the near-concentric regime face a tradeoff between mechanical stability and high single-atom cooperativity. To overcome this limitation, we design and implement a geometrically asymmetric standing-wave cavity. This structure, with mirrors of very different radii of curvature, allows strong atom-light coupling while exhibiting good stability against misalignment. We observe effective cooperativities ranging from ${\eta }_{\mathrm{eff}}=10$ to ${\eta }_{\mathrm{eff}}=0.2$ by shifting the location of the atoms in the cavity mode. By loading ${}^{171}\mathrm{Yb}$ atoms directly from a mirror magneto-optical trap into a one-dimensional optical lattice along the cavity mode, we produce atomic ensembles with collective cooperativities up to $N\eta =2\times {10}^4$. This system opens a way to preparing spin squeezing for an optical lattice clock and to accessing a range of nonclassical collective states.

Fractals, complex shapes with structure at multiple scales, have long been observed in nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains, and coastlines. With their highly polished spherical mirrors, laser resonators are almost the precise opposite of nature, and so it came as a surprise when, in 1998, transverse intensity cross sections of the eigenmodes of unstable canonical resonators were predicted to be fractals [G. P. Karman et al., Nature (London) 402, 138 (1999)]. Experimental verification has so far remained elusive. Here we observe a variety of fractal shapes in transverse intensity cross sections through the lowest-loss eigenmodes of unstable canonical laser resonators, thereby demonstrating the controlled generation of fractal light inside a laser cavity. We also advance the existing theory of fractal laser modes, first by predicting three-dimensional self-similar fractal structure around the center of the magnified self-conjugate plane and second by showing, quantitatively, that intensity cross sections are most self-similar in the magnified self-conjugate plane. Our work offers a significant advance in the understanding of a fundamental symmetry of nature as found in lasers.

Entanglement is a unique resource for quantum-enhanced applications. When employed in sensing, shared entanglement between distributed quantum sensors enables a substantial gain in the measurement sensitivity in estimating global parameters of the quantum sensor network. Loss incurred in the distribution of entanglement, however, quickly dissipates the measurement-sensitivity advantage enjoyed by the entangled quantum sensors over sensors supplied with local quantum resources. Here we present a viable approach to overcome the entanglement-distribution loss and show that the measurement sensitivity enabled by entangled quantum sensors beats that afforded by the optimum local resource. Our approach relies on noiseless linear amplifiers (NLAs) to serve as quantum repeaters. We show that, unlike the outstanding challenge of building quantum repeaters to suppress the repeaterless bound for quantum key distribution, NLA-based quantum repeaters for distributed quantum sensing are realizable by available technology. As such, distributed quantum sensing would become an application instance that benefits from quantum repeaters.

Ab initio QED calculations of the four x-ray transitions from the $L$ to $K$ shell in heliumlike argon, titanium, iron, copper, and krypton are performed. The binding energies for all the $n=1$ and $n=2$ states are evaluated as well. The calculation approach combines the rigorous QED treatment in the first two orders of the perturbation theory constructed within the extended Furry picture with the third- and higher-order correlation effects evaluated in the Breit approximation. The obtained results are compared with the previous evaluations and available experimental data.

We study the modification of the atomic spontaneous emission rate, i.e., the Purcell effect, of ${}^{87}\mathrm{Rb}$ in the vicinity of an optical nanofiber ($\sim 500$ nm diameter). We observe enhancement and inhibition of the atomic decay rate depending on the alignment of the induced atomic dipole relative to the nanofiber. We present calculations with two different methods that qualitatively agree with some of the results; the calculations that best agree consider the atoms as simple oscillating dipoles. This is surprising since the multilevel nature of the atoms should produce a different radiation pattern, predicting different modification of the lifetime than the measured ones. This work is a step towards characterizing and controlling atomic properties near optical waveguides, fundamental tools for the development of quantum photonics.

Photonic states of high-$Q$ superconducting microwave cavities controlled by superconducting transmon ancillas provide a platform for encoding and manipulating quantum information. A key challenge in scaling up the platform towards practical quantum computation is the requirement to communicate on demand the quantum information stored in the cavities. It has been recently demonstrated that a tunable bilinear interaction between two cavity modes can be realized by coupling the modes to a bichromatically driven superconducting transmon ancilla, which allows swapping and interfering the multiphoton states stored in the cavity modes [Gao et al., Phys. Rev. X 8, 021073 (2018)]. Here we explore both theoretically and experimentally the regime of relatively strong drives on the ancilla needed to achieve fast swap gates but which can also lead to undesired nonperturbative effects that lower the swap fidelity. We develop a theoretical formalism based on linear response theory that allows one to calculate the rate of ancilla-induced interaction, decay, and frequency shift of the cavity modes in terms of a susceptibility matrix. We go beyond the usual perturbative treatment of the drives by using Floquet theory, and find that the interference of the two drives can strongly alter the system dynamics even in the regime where the standard rotating wave approximation applies. The drive-induced ac Stark shift on the ancilla depends nontrivially on the drive and ancilla parameters which in turn modify the strength of the engineered interaction. We identify two major sources of infidelity due to ancilla decoherence. (i) Ancilla dissipation and dephasing lead to incoherent hopping among Floquet states which occurs even when the ancilla is at zero temperature; this hopping results in a sudden change of the swap rate, thereby decohering the swap operation. (ii) The cavity modes inherit finite decay from the relatively lossy ancilla through the inverse Purcell effect; the effect becomes particularly strong when the ac Stark shift pushes certain ancilla transition frequencies to the vicinity of the cavity mode frequencies. The theoretical predictions agree quantitatively with the experimental results, paving the way for using the developed theory for optimizing future experiments and architecture designs.