In this work, we consider the estimation of single-mode Gaussian states using four different measurement schemes, namely, (1) homodyne measurement, (2) heterodyne measurement, (3) sequential measurement scheme, and (4) the Arthurs-Kelly measurement scheme, with a view to compare their relative performance. To this end, we work in the phase space formalism, specifically at the covariance matrix level, which provides an elegant and intuitive way to explicitly carry out the involved calculations. We show that the optimal performance of the Arthurs-Kelly and sequential measurement schemes is equal to the heterodyne measurement. While the heterodyne measurement outperforms the homodyne measurement in the mean estimation of squeezed state ensembles, the homodyne measurement outperforms the heterodyne measurement for variance estimation of squeezed state ensembles up to a certain range of the squeezing parameter. We then modify the Hamiltonian in the Arthurs-Kelly measurement scheme, such that the two meters can have correlations and show that the optimal performance is achieved when the meters are uncorrelated. We expect that these results will be useful in various quantum information and quantum communication protocols.

We demonstrate that the output statistics of a standard quantum annealing protocol run on D-Wave 2000Q can be mimicked by static disorder garnishing an otherwise ideal device hardware – for a 10-qubit toy Hamiltonian as well as for problem instances with thousands of qubits. A Boltzmann-like distribution over distinct output states is shown to emerge with increasing disorder strength.

Optical quantum memories, which store and preserve the quantum state of photons, rely on a coherent mapping of the photonic state onto matter states that are optically accessible. Here we outline and characterize schemes to map the state of photons onto long-lived but optically inaccessible collective states of noble-gas spins. The mapping employs coherent spin-exchange interaction arising from random collisions with alkali vapor. We propose efficient storage strategies in two operating regimes and analyze their performance for several proposed experimental configurations.

We study the enantiospecific state transfer for gaseous symmetric-top chiral molecules by constructing a four-level model. This model is formed by coupling the electric dipole transitions among four appropriate rovibrational states with three electromagnetic fields. It includes two cyclic three-level substructures, where the overall phases of the coupling strengths differ by $\pi$ with enantiomers and reflect the chirality dependence of the molecules. Based on this four-level model, two dynamic ways are proposed to achieve the approximately perfect enantiospecific state transfer for gaseous symmetric-top chiral molecules when all the molecules are initially in the ground state of the system.

The unitary transformation method is used to study the properties of the polaritonic states and Bose-Einstein condensation in the Rabi lattice model, where the on-site two-level systems (TLSs) are coupled with the intersite hopping photons. It is shown that the counter-rotating coupling (CRC) between TLS and photon, which breaks down the conservation of the excitation numbers, may induce a long-range Ising-like interaction among intersite TLSs. We have shown that the coupled TLSs and photons are hybridized to form the polaritonic states, and the corresponding ground state and polaritonic excitation spectra are calculated by diagonalizing our transformed Hamiltonian. When the photon hopping $J$ is weak, the excitation spectrum is gapped. But the gap decreases with increasing $J$, and at critical value $J=J_c$ the gap becomes zero at the $\mathrm{\Gamma }$ point and the ground state becomes instable. Thus, $J_c$ is the phase transition point where the polaritons are condensed at the $\mathrm{\Gamma }$ point to form the delocalized superradiant phase. The results show that the larger detuning between TLS and photon favors the disorder insulator phase, which requires the stronger $J_c$ to get the long-range order phase. The phase diagram of the delocalized superradiant phase transition has been obtained where there are no Mott lobes since the CRC breaks down the number conservation. The ground state and the excitation spectra of the delocalized superradiant phase are also calculated. It is shown that in the delocalized superradiant state the order parameter is the nonzero ground-state average of the photon annihilation operator. The polaritonic excitation has a finite excitation gap because the CRC breaks down the number conservation but leaves only a discrete symmetry, the parity conservation.

We study Smith-Purcell radiation from a conducting grating generated by an inclined passage of a shaped electron wave packet with an electric quadrupole moment in the nonparaxial regime. Spreading of an asymmetric wave packet induces quadrupole corrections to the radiation field. Although the nonparaxial corrections stay small, they are dynamically enhanced during the interaction of the electron with the grating whose length exceeds the Rayleigh length of the packet. To simplify the possible experimental setup where such effects could be measured, we study the dependence of these effects on the inclination angle, i.e., the angle between the mean velocity of the packet and the surface of the grating. There is a minimal angle such that the multipole expansion always stays valid at the grating surface. In such a regime, the quadrupole contribution to the Smith-Purcell radiation can become the leading one, which represents a quantum effect impossible for classical pointlike electrons. Thus, the impact of the wave-packet shape (vortex structure or nonspherical shape) can be observed experimentally by comparing the radiation for different orientations of the grating in the single-electron regime.

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocality in time associated with the modular energy operator. Some applications of our formalization are provided through illustrative examples.

We explore sufficient conditions for inseparability in mixed states with a globally conserved charge, such as a particle number. We argue that even separable states may contain entanglement in fixed charge sectors, as long as the state cannot be separated into charge-conserving components. As a witness of symmetric inseparability we study the number entanglement (NE), $\mathrm{\Delta }{S}_m$, defined as the entropy change due to a subsystem's charge measurement. Whenever $\mathrm{\Delta }{S}_m>0$, there exist inseparable charge sectors, having finite (logarithmic) negativity, even when the full state either is separable or has vanishing negativity. We demonstrate that the NE is not only a witness of symmetric inseparability, but also an entanglement monotone. Finally, we study the scaling of $\mathrm{\Delta }{S}_m$ in thermal one-dimensional systems combining high-temperature expansion and conformal field theory.

Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph states to be in TQO-1, which is a class of quantum error-correction code states whose code distance scales macroscopically with the number of physical qubits. Using these criteria, we consider a number of specific graph families, including the star and complete graphs, and the line graphs of complete and completely bipartite graphs, and discuss which are topologically ordered and how to construct the codewords. The formalism is then employed to construct several codes with macroscopic distance, including a three-dimensional topological code generated by local stabilizers that also has a macroscopic number of encoded logical qubits. The results indicate that graph states provide a fruitful approach to the construction and characterization of topological stabilizer quantum error-correction codes.

In the Bennett-Brassard 1984 protocol, we optimize the ratio of the choice of two bases, the bit basis and the phase basis, by using the second-order expansion for the length of the generation keys under the coherent attack. This optimization addresses the trade-off between the loss of transmitted bits due to the disagreement of their bases and the estimation error of the error rate in the phase basis. Then, we derive the optimum ratio and the optimum length of the generation keys with the second-order asymptotics. Surprisingly, the second order has the order $n^{\frac{3}{4}}$, which is much larger than the second-order $n^{\frac{1}{2}}$ in the conventional setting when $n$ is the number of quantum communication. This fact shows that our setting has much larger importance for the second-order analysis than the conventional problem. To illustrate this importance, we numerically plot the effect of the second-order correction.

Cryptanalysis of quantum cryptographic systems generally involves finding optimal adversarial attack strategies on the underlying protocols. The core principle of modeling quantum attacks often reduces to the ability of the adversary to clone unknown quantum states and to extract thereby meaningful secret information. Explicit optimal attack strategies typically require high computational resources due to large circuit depths or, in many cases, are unknown. Here we introduce variational quantum cloning (VarQlone), a cryptanalysis algorithm based on quantum machine learning, which allows an adversary to obtain optimal approximate cloning strategies with short depth quantum circuits, trained using hybrid classical-quantum techniques. The algorithm contains operationally meaningful cost functions with theoretical guarantees, quantum circuit structure learning and gradient-descent-based optimization. Our approach enables the end-to-end discovery of hardware-efficient quantum circuits to clone specific families of quantum states, which we demonstrate in an implementation on the Rigetti Aspen quantum hardware. We connect these results to quantum cryptographic primitives and derive explicit attacks facilitated by VarQlone. We expect that quantum machine learning will serve as a resource for improving attacks on current and future quantum cryptographic protocols.

The nonlinear Zeeman effect can induce splittings and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. We demonstrate an all-optical scheme, based on spin locking, to suppress the nonlinear Zeeman effect. This scheme achieves spin locking via an effective oscillating magnetic field in the form of AC Stark shifts induced by an intensity- and polarization-modulated laser beam. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with $\sim 100\mathrm{Hz}$ width in the Earth-field range into a peak with a central component width of 25 Hz. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude and decreasing its width. An advantage of the all-optical approach is the absence of crosstalk between nearby sensors when they are used in a gradiometric or array arrangement.

The spatial structure of a two-dimensional homogeneous mixture of fermionic atoms in two hyperfine states is analyzed throughout the BEC-BCS crossover. Within the BCS-Leggett mean-field model we consider three functions: the pair wave function and the density-density correlation functions between atoms of the same and of different hyperfine states. For the correlation functions we derive analytical expressions which allow one to unveil the rich spatial structure of the superfluid. Mainly, we are able to study the large-distance behavior of the three functions, which exhibits an exponential decay and a well-defined oscillatory behavior. We report closed-form expressions for the correlation lengths and mean pair radius. Differences and similarities emerge when comparing with the three-dimensional case. Particularly, we find an expression for the large-distance correlation length, in terms of the chemical potential and the gap, valid in two and three dimensions, but whose dependence on the corresponding scattering lengths differ significantly.

We investigate the dynamics of heavy impurities embedded in an ultracold Fermi gas by using a generalized Langevin equation. The latter—derived by means of influence functional theory—describes how the stochastic classical dynamics of the impurities and the quantum nature of the fermionic bath manifests in the emergent interaction between the impurities and in the viscosity tensor. By focusing on the two-impurity case, we predict the existence of bound states, in different conditions of coupling and temperature, whose lifetime can be analytically estimated. Our predictions should be testable using cold-gases platforms within current technology.

Owing to their highly coherent emission and compact form factor, Brillouin lasers have been identified as a valuable asset for applications including portable atomic clocks, precision sensors, coherent microwave synthesis, and energy-efficient approaches to coherent communications. While the fundamental emission linewidth of these lasers can be very narrow, noise within dielectric materials leads to drift in the carrier frequency, posing vexing challenges for applications requiring ultrastable emission. A unified understanding of Brillouin laser performance may provide critical insights to reach new levels of frequency stability; however, existing noise models focus on only one or a few key noise sources, and do not capture the thermo-optic drift in the laser frequency produced by thermal fluctuations or absorbed power. Here, we develop a coupled-mode theory of Brillouin laser dynamics that accounts for dominant forms of noise in noncrystalline systems, capturing the salient features of the frequency and intensity noise for a variety of systems. As a result, theory and experiment can be directly compared to identify key sources of noise and the frequency bands they impact, revealing strategies to improve the performance of Brillouin lasers and pave the way for highly coherent sources of light on a chip.

Motivated by the emergence of stacked two-dimensional materials with a twist angle, we examine the photonic spin Hall effect in twisted few-layer anisotropic two-dimensional atomic crystals. By developing a generalized model for arbitrary layers of anisotropic two-dimensional atomic crystals, the photonic spin Hall effect of twisted few-layer black phosphorus without interlayer interaction is demonstrated and discussed. We find that the twist between different layers results in the arise of the in-plane spin Hall shift, and the shift is very sensitive to the twist angle. While the in-plane spin Hall shifts are symmetric about the origin as a function versus the twist angle, the transverse spin Hall shifts are symmetric about the axis. And the photonic spin Hall shifts exhibit periodic changes versus the thickness of the interlayer due to the optical Fabry-Pérot resonance. The results may provide different aspects for analysis and control of the optical properties of twisted multilayer two-dimensional materials.

In this article we present an experimental proposal for the estimation of an optomechanical parameter in the presence of noise. The estimation is based on the technique of weak-value amplification which can enlarge the radiation pressure effect of a single photon on a mechanical oscillator. In our setup we show that the weak-value amplification technique is preferable for the estimation over a method that relies on a strong measurement with postselection because the first method does not require a good prior knowledge of the parameter we wish to estimate, while both strategies reach the same level of precision from a Fisher information perspective. In the presence of strongly correlated noise, the weak-value amplification method is preferable, from a Fisher information perspective, than a standard measurement strategy that does not employ postselection and that is affected by the same type of noise.

The response of the level anticrossing signal to a quasiresonant radio-frequency field, which appears in a zero magnetic field at nitrogen-vacancy (NV) color centers in diamond, is investigated. It is shown that the complex structure of this response can be explained by the Autler-Townes splitting. The possibility of controlling the parameters of the level anticrossing signal is considered. It is shown that the slope of the central resonance recorded in this structure upon low-frequency modulation of the external magnetic field can be 2.3 times higher than the slope of the resonance recorded in the absence of a radio-frequency field. Conclusions are drawn about the nature of the level anticrossing effect arising in zero field in NV color centers in diamond.

It is shown that electron backscattering can enhance high-order-harmonic generation in periodic systems with broken translational symmetry. Paradigmatically, we derive for a finite chain of atoms the harmonic cutoff due to electrons backscattered from the edges of the chain and demonstrate a maximum in the harmonic yield if twice the quiver amplitude of the driven electrons equals the chain length. For an intuitive understanding of our quantum results we develop a refined semiclassical trajectory model with finite electron-hole separation after tunneling. We demonstrate that the same “tunnel exit” also holds for interband harmonics in conventional periodic solid-state systems.