We investigate the dynamics of a Bose-Einstein condensate of magnetic atoms in which the dipoles are rotated by an external magnetic field. The time-averaged dipole-dipole interaction between the atoms is effectively tuned by this rotation, however, recent experimental and theoretical developments show that dynamic instabilities emerge that may cause heating. We present simulations of a realistic tuning sequence in this system, and characterize the system behavior and the emergence of instabilities. Our results indicate that the instabilities develop more slowly as the rotation frequency increases, and indicate that experiments with tuned dipole-dipole interactions should be feasible.

For every stabilizer $N$-qudit absolutely maximally entangled state, we present a method for determining the stabilizer generators and logical operators of a corresponding quantum error-correction code. These codes encode $k$ qudits into $N-k$ qudits, with $k\le \lfloor N/2\rfloor$, where the local dimension $d$ is prime. We use these methods to analyze the concatenation of such quantum codes and link this procedure to entanglement swapping. Using our techniques, we investigate the spread of quantum information on a tensor network code formerly used as a toy model for the AdS/CFT correspondence. In this network, we show how corrections arise to the Ryu-Takayanagi formula in the case of entangled input state, and that the bound on the entanglement entropy of the boundary state is saturated for absolutely maximally entangled input states.

We study the feasibility of meaningful proof-of-principle demonstrations of several quantum repeater protocols with photon (single-photon and photon-pair) sources and atomic-ensemble-based quantum memories. We take into account nonunit memory efficiencies that decay exponentially with time, which complicates the calculation of repeater rates. We discuss implementations based on quantum dots, parametric downconversion, rare-earth-ion doped crystals, and Rydberg atoms. Our results provide guidance for the near-term implementation of long-distance quantum repeater demonstrations, suggesting that such demonstrations are within reach of current technology.

The ability to generate and verify multipartite entanglement is an important benchmark for near-term quantum devices. We develop a scalable entanglement metric based on multiple quantum coherences and demonstrate experimentally on a 20-qubit superconducting device. We report a state fidelity of $0.5165\pm 0.0036$ for an 18-qubit GHZ state, indicating multipartite entanglement across all 18 qubits. Our entanglement metric is robust to noise and only requires measuring the population in the ground state; it can be readily applied to other quantum devices to verify multipartite entanglement.

Cooper minimum structure of high-order harmonic spectra from atoms or molecules has been extensively studied. In this paper, we demonstrate that the crystal harmonic spectra from an ultrashort midinfrared laser pulse also exhibit the Cooper minimum characteristic. Based on the accurate band dispersion and $k$-dependent transition dipole moment (TDM) from the first-principles calculations, it can be found that the harmonic spectra from the MgO crystal along the $\mathrm{\Gamma }\text{−}X$ direction present a dip structure in the plateau, which is originated from the valley of TDM by examining the distribution of the harmonic intensity at the $k$ space. The Cooper minimum feature in crystal high-order-harmonic generation (HHG) will pave a new way to retrieve the band information of solid materials by using HHG from the ultrashort midinfrared laser pulse.

Variational quantum circuits are becoming tools of choice in quantum optimization and machine learning. In this paper we investigate a class of variational circuits for the purposes of supervised machine learning. We propose a circuit architecture suitable for predicting class labels of quantumly encoded data via measurements of certain observables. We observe that the required depth of a trainable classification circuit is related to the number of representative principal components of the data distribution. Quantum circuit architectures used in our design are validated by numerical simulation, which shows significant model size reduction compared to classical predictive models. Circuit-based models demonstrate good resilience to noise, which makes then robust and error tolerant.

We theoretically analyze superradiant emission of light from a cold atomic gas, when mechanical effects of photon-atom interactions are considered. The atoms are confined within a standing-wave resonator and an atomic metastable dipolar transition couples to a cavity mode. The atomic dipole is incoherently pumped in the parameter regime that would correspond to stationary superradiance in the absence of inhomogeneous broadening. Starting from the master equation for cavity field and atomic degrees of freedom we derive a mean-field model that allows us to determine a threshold temperature, above which thermal fluctuations suppress superradiant emission. We then analyze the dynamics of superradiant emission when the motion is described by a mean-field model. In the semiclassical regime and below the threshold temperature we observe that the emitted light can be either coherent or chaotic, depending on the incoherent pump rate. We then analyze superradiant emission from an ideal Bose gas at zero temperature when the superradiant decay rate $\mathrm{\Lambda }$ is on the order of the recoil frequency ${\omega }_R$. We show that the quantized exchange of mechanical energy between the atoms and the field gives rise to a threshold, ${\mathrm{\Lambda }}_c$, below which superradiant emission is damped down to zero. When $\mathrm{\Lambda }>{\mathrm{\Lambda }}_c$ superradiant emission is accompanied by the formation of matter-wave gratings diffracting the emitted photons. The stability of these gratings depends on the incoherent pump rate $w$ with respect to a second threshold value $w_c$. For $w>w_c$ the gratings are stable and the system achieves stationary superradiance. Below this threshold the coupled dynamics becomes chaotic. We characterize the dynamics across these two thresholds and show that the three phases we predict (incoherent, coherent, chaotic) can be revealed via the coherence properties of the light at the cavity output.

We propose and demonstrate a method to increase the momentum separation between the arms of an atom interferometer and thus its area and measurement precision, by using Bloch oscillations (BOs) in an excited band of a pulsed optical standing-wave lattice. Using excited bands allows us to operate at particular “magic” depths, where high momentum-transfer efficiency ($>99.4\%$ per $\hslash k$, where $\hslash k$ is the photon momentum) is maintained while minimizing the lattice-induced phase fluctuations ($<1\mathrm{mrad}$ per $\hslash k$) that are unavoidable in ground-band BOs. We apply this method to demonstrate interferometry with up to $40\hslash k$ momenta supplied by BOs. We discuss extensions of this technique to larger momentum transfer and adaptations towards metrological applications of atom interferometry such as a measurement of the fine-structure constant.

The collective spontaneous emission of two point-dipole emitters near a plasmonic core-shell nanosphere is theoretically investigated. Based on the expansion of mode functions in vector spherical harmonics, we derive closed analytical expressions for both the cooperative decay rate and the dipole-dipole interaction strength associated with two point dipoles close to a sphere. Considering a plasmonic nanoshell containing a linearly amplifying medium inside the core, the second-order correlation function for the two emitters shows that it is possible to tune the photon emission, selecting either photon bunching or antibunching as a function of the polarization and position of the sphere. This result opens vistas to applications involving tunable single-photon sources in engineered artificial media.

We investigate a quantum spatial search problem on fractal lattices, such as Sierpinski carpets and Menger sponges. In earlier numerical studies of the Sierpinski gasket, the Sierpinski tetrahedron, and the Sierpinski carpet, conjectures have been proposed for the scaling of a quantum spatial search problem finding a specific target, which is given in terms of the characteristic quantities of a fractal geometry. We find that our simulation results for extended Sierpinski carpets and Menger sponges support the conjecture for the optimal number of oracle calls, where the exponent is given by $1/2$ for $d_{\mathrm{s}}>2$ and the inverse of the spectral dimension $d_{\mathrm{s}}$ for $d_{\mathrm{s}}<2$. We also propose a scaling hypothesis for the effective number of oracle calls defined by the ratio of the optimal number of oracle calls to a square root of the maximum finding probability. The form of the scaling hypothesis for extended Sierpinski carpets is very similar but slightly different from the earlier conjecture for the Sierpinski gasket, the Sierpinski tetrahedron, and the conventional Sierpinski carpet.

Carrier-envelope and optical phase noise of a femtosecond frequency comb based on Er-doped fiber technology is investigated and minimized without exploiting active external references. Ultrabroadband, coherent, and tailorable supercontinua are generated in a highly nonlinear germanosilicate fiber assembly. Difference frequency mixing between comb modes in their spectral extrema passively eliminates the carrier-envelope phase slip. This step generates an inherently offset-free comb with a relative frequency stability better than ${10}^{-21}$. In contrast, the phase fluctuations at the carrier frequency of 193 THz are increased as compared to the fundamental comb. Their level matches the value found by parabolic extrapolation of the phase noise of the fundamental comb to zero frequency. The latter is unambiguously accessible by means of any beat note centered at the carrier-envelope offset frequency. All these findings rely on strong correlations between the comb modes that are quantitatively described by an elastic tape model, underlining the deterministic character of the processes involved. The superior optical phase noise of the fundamental comb is transferred to the difference-frequency comb while not compromising the inherent cancellation of the carrier-envelope offset frequency. In this way, the optical linewidth of the passively phase-locked comb is reduced from 100 kHz to a measured value of 5 kHz, which is limited by the cw laser reference used for out-of-loop characterization.

In recent years, cold atoms could prove their scientific impact not only on ground but in microgravity environments such as the drop tower in Bremen, sounding rockets, and parabolic flights. We investigate the preparation of cold atoms in an optical dipole trap, with an emphasis on evaporative cooling under microgravity. Up to $1\times {10}^6$ rubidium-87 atoms were optically trapped from a temporarily dark magneto-optical trap during free fall in the drop tower in Bremen. The efficiency of evaporation is determined to be equal with and without the effect of gravity. This is confirmed using numerical simulations that prove the dimension of evaporation to be three dimensional in both cases due to the anharmonicity of optical potentials. These findings pave the way towards various experiments on ultracold atoms under microgravity and support other existing experiments based on atom chips but with plans for additional optical dipole traps such as the upcoming follow-up missions to past and current space-borne experiments.

We compute the frequency-dependent shear and bulk viscosity spectral functions of an interacting Fermi gas in a quantum virial expansion up to second quadratic order in the fugacity parameter $z=e^{\beta \mu }$, which is small at high temperatures. Calculations are carried out using a diagrammatic finite-temperature field-theoretic framework, in which the analytic continuation from Matsubara to real frequencies is carried out in closed analytic form. Besides a possible zero-frequency Drude peak, our results for the spectral functions show a broad continuous spectrum at all frequencies with an additional bound-state contribution for frequencies larger than the dimer-breaking energy. Our results are consistent with various sum rules and universal high-frequency tails. In the low-frequency limit, the shear viscosity spectral function is recast as a collision integral, which reproduces known results for the static shear viscosity from kinetic theory. Our findings for the static bulk viscosity of a Fermi gas near unitarity, however, show a nonanalytic dependence on the scattering length, at variance with kinetic theory.

We study the dark-time decay of the retrieval efficiency for light stored in a Rydberg state in an ultracold gas of ${}^{87}\mathrm{Rb}$ atoms based on electromagnetically induced transparency (EIT). Using low atomic density to avoid dephasing caused by atom-atom interactions, we measure a $1/e$ time of $30\mu \mathrm{s}$ for the $80S$ state in free expansion. One of the dominant limitations is the combination of photon recoil and thermal atomic motion at $0.2\mu \mathrm{K}$. If the 1064-nm dipole trap is left on, then the $1/e$ time is reduced to $13\mu \mathrm{s}$, in agreement with a model taking differential light shifts and gravitational sag into account. To characterize how coherent the retrieved light is, we overlap it with reference light and measure the visibility $V$ of the resulting interference pattern, obtaining $V>90\%$ for short dark time. Our experimental work is accompanied by a detailed model for the dark-time decay of the retrieval efficiency of light stored in atomic ensembles. The model is generally applicable for photon storage in Dicke states, such as in EIT with $\mathrm{\Lambda }$-type or ladder-type level schemes and in Duan-Lukin-Cirac-Zoller single-photon sources. The model includes a treatment of the dephasing caused by thermal atomic motion combined with net photon recoil, as well as the influence of trapping potentials. It takes into account that the signal light field is typically not a plane wave. The model maps the retrieval efficiency to single-atom properties and shows that the retrieval efficiency is related to the decay of fringe visibility in Ramsey spectroscopy and to the spatial first-order coherence function of the gas.

We study experimentally and theoretically the time-dependent response of a cold atom cloud illuminated by a laser beam immediately after the light is switched on. We show that cooperative effects, which have been previously investigated in the decay dynamics after the laser is switched off, also give rise to characteristic features in this configuration. In particular, we show that collective Rabi oscillations exhibit a superradiant damping. We first consider an experiment that is performed in the linear-optics regime and is well described by a linear coupled-dipole theory. We then show that this linear-optics model breaks down when increasing the saturation parameter, and that the experimental results are then well described by a nonlinear mean-field theory.

Bosonic quantum error correction is a viable option for realizing error-corrected quantum information processing in continuous-variable bosonic systems. Various single-mode bosonic quantum error-correcting codes such as cat, binomial, and Gottesman-Kitaev-Preskill (GKP) codes have been implemented experimentally in circuit QED and trapped-ion systems. Moreover, there have been many theoretical proposals to scale up such single-mode bosonic codes to realize large-scale fault-tolerant quantum computation. Here, we consider the concatenation of the single-mode GKP code with the surface code, namely, the surface-GKP code. In particular, we thoroughly investigate the performance of the surface-GKP code by assuming realistic GKP states with a finite squeezing and noisy circuit elements due to photon losses. By using a minimum-weight perfect matching decoding algorithm on a three-dimensional spacetime graph, we show that fault-tolerant quantum error correction is possible with the surface-GKP code if the squeezing of the GKP states is higher than 11.2 dB in the case where the GKP states are the only noisy elements. We also show that the squeezing threshold changes to 18.6 dB when both the GKP states and circuit elements are comparably noisy. At this threshold, each circuit component fails with probability $0.69\%$. Finally, if the GKP states are noiseless, fault-tolerant quantum error correction with the surface-GKP code is possible if each circuit element fails with probability less than $0.81\%$. We stress that our decoding scheme uses the additional information from GKP-stabilizer measurements and we provide a simple method to compute renormalized edge weights of the matching graphs. Furthermore, our noise model is general because it includes full circuit-level noise.

Entanglement, while being critical in many quantum applications, is difficult to characterize experimentally. While entanglement witnesses based on the fidelity to the target entangled state are efficient detectors of entanglement, they in general underestimate the amount of entanglement due to local unitary errors during state preparation and measurement. Therefore, to detect entanglement more robustly in the presence of such control errors, we introduce a ‘subspace’ witness that detects a broader class of entangled states with strictly larger violation than the conventional state-fidelity witness at the cost of additional measurements, while remaining more efficient with respect to state tomography. We experimentally demonstrate the advantages of the subspace witness by generating and detecting entanglement with a hybrid, two-qubit system composed of electronic spins in diamond. We further extend the notion of the subspace witness to specific genuine multipartite entangled (GME) states detected by the state witness, such as GHZ, $W$, and Dicke states, and motivate the choice of the metric based on quantum information tasks, such as entanglement-enhanced sensing. In addition, as the subspace witness identifies the many-body coherences of the target entangled state, it facilitates (beyond detection) lower-bound quantification of entanglement via generalized concurrences. We expect that the straightforward and efficient implementation of subspace witnesses would be beneficial in detecting specific GME states in noisy, intermediate-scale quantum processors with a hundred qubits.

We measure the interspecies interaction strength between ${}^7\mathrm{Li}$ and ${}^{87}\mathrm{Rb}$ atoms through cross-dimensional relaxation of two-element gas mixtures trapped in a spherical-quadrupole magnetic trap. We record the relaxation of an initial momentum-space anisotropy in a lithium gas when cotrapped with rubidium atoms, with both species in the $|F=1,m_F=-1\rangle$ hyperfine state. Our measurements are calibrated by observing cross-dimensional relaxation of a ${}^{87}\mathrm{Rb}$-only trapped gas. Through Monte Carlo simulations, we compare the observed relaxation to that expected given the theoretically predicted energy-dependent differential cross section for ${}^7\mathrm{Li}\text{−}{}^{87}\mathrm{Rb}$ collisions. The experimentally observed relaxation occurs significantly faster than predicted theoretically, a deviation that appears incompatible with other experimental data characterizing the ${}^7\mathrm{Li}\text{−}{}^{87}\mathrm{Rb}$ molecular potential.

Recent experiments have revitalized the interest in a Fermi gas of ultracold atoms with strong repulsive interactions. In spite of its seeming simplicity, this system exhibits a complex behavior, resulting from the competing action of two distinct instabilities: ferromagnetism, which promotes spin anticorrelations and domain formation; and pairing, which renders the repulsive fermionic atoms unstable toward forming weakly bound bosonic molecules. The breakdown of the homogeneous repulsive Fermi liquid arising from such concurrent mechanisms has been recently observed in real time through pump-probe spectroscopic techniques [A. Amico et al., Phys. Rev. Lett. 121, 253602 (2018)]. These studies also lead to the discovery of an emergent metastable many-body state, an unpredicted quantum emulsion of anticorrelated fermions and pairs. Here, we investigate in detail the properties of such an exotic regime by studying the evolution of kinetic and release energies, the spectral response and coherence of the unpaired fermionic population, and its spin-density noise correlations. All our observations consistently point to a low-temperature heterogeneous phase, where paired and unpaired fermions macroscopically coexist while featuring microscale phase separation. Our findings open appealing avenues for the exploration of quantum emulsions and also possibly of inhomogeneous superfluid regimes, where pair condensation may coexist with magnetic order.

Violation of linearity of the King plot is investigated for a chain of partially stripped argon isotopes. The nonlinearity originates within the standard model from subtle contributions to the isotope shifts from next-to-leading order effects, which have never been systematically studied so far. In light atoms these nonlinear effects are dominated by the quadratic nuclear recoil ($\propto 1/M^2$, where $M$ is the nuclear mass). Large-scale relativistic calculations of the linear and quadratic mass shift and the field shift are performed for the $2P$ fine-structure transitions in Be-like, B-like, and C-like argon ions. Nonlinearities of the King plots from 5 to 30 kHz are found, which is four orders of magnitude larger than previous estimates in comparable systems. Accurate calculations of these effects are vital for identification of possible nonlinearities originating from physics beyond the standard model.