Frenkel excitons are of interest for ultrafast switching applications due to the femtosecond timescale at which coherent exciton transfer between chromophores takes place. The Frenkel Hamiltonian, which governs the dynamics of Frenkel excitons, belongs to a class of Hamiltonians that enable universal quantum computation. It is thus of interest to determine how a complete set of exciton-based gates for quantum computing could be constructed as aggregates of chromophores. We demonstrate that a controlled phase shifter can be constructed as a pair of exciton transmission lines that employ two types of chromophores and that are cross coupled by a two-exciton interaction. This element facilitates the construction of controlled basis-change gates, thereby enabling the implementation of a complete set of exciton-based gates for universal quantum computation.

We propose a concise and deterministic protocol to generate NOON states in a hybrid system consisting of a superconducting qubit, a circuit resonator mode, and two magnonic modes, based on Floquet engineering. In particular, we construct a time-reversal-symmetry broken Hamiltonian for chiral state propagation of the three continuous-variable modes depending on qubit state, by the time modulation over qubit-resonator interaction and magnon frequency. Then, an arbitrary magnonic NOON state can be generated by a typical preparing-and-measurement procedure. We analyze the robustness of our protocol against the systematic errors in the qubit-magnon coupling strength, the Floquet-driving intensity, the frequency mismatch of the magnons, and the counterrotating interactions. We can obtain a high-fidelity NOON state in the presence of quantum dissipation on all components.

We theoretically study quantum-optical properties of one- and two-dimensional semiconductor nanostructures, where the electronic band structure is described by a two-band tight-binding model. Since the focus of our work is on analyzing quantum-optical effects of systems with a continuous band structure, many-body processes like electron-electron and electron-phonon interactions are neglected. The quantum-optical interband excitations are fully incorporated and described by a Jaynes-Cummings-type model. The exciting quantum light can be a state with arbitrary photon statistics. For simplicity, the results discussed here are limited to single-photon and two-photon Fock states. Our analytical approach is based on the eigenvalue problem and can be utilized to obtain explicit expressions for the steady-state properties of the system. Numerical simulations are based on solutions of the equations of motion and allow for a more precise analysis of the dynamics and nonresonant excitations of the system. We demonstrate that during the interaction process, a collective excitation of the conduction band is formed. For nonresonant excitations, this collective dynamics results in interesting steady states, in which the resonantly addressed eigenstates are occupied. The presented model provides a framework for microscopic simulations of quantum-optically excited extended semiconductor nanostructures.

In this paper we analyze the notion of measurement noncontextuality (MNC) and identify contextual scenarios which involve sequential measurements of only a single measurement device. We show that any noncontextual ontological model fails to explain the statistics of outcomes of a single carefully constructed positive-operator-valued measure (POVM) executed sequentially on a quantum system. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the noncontextual (NC) ontic model, and construct a quantum situation involving measurements from the Klyachko-Can-Binicioǧlu-Shumovsky (KCBS) inequality. We show that the resultant statistics arising from this device violate our NC inequality. This device can be generalized by incorporating measurements from arbitrary $n$-cycle contextuality inequalities of which $n=5$ corresponds to the KCBS inequality. We show that the NC and quantum bounds for various scenarios can be derived more easily using only the functional relationships between the outcomes for larger values $n$. This makes it one of the simpler contextual inequalities to analyze.

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- $(\mathcal{PT}-)$ and $\mathrm{anti}-\mathcal{PT}-\mathrm{symmetric}$ physics have gained ever-growing interest, due to the existence of non-Hermitian spectral singularities called exceptional points (EPs). On the other hand, topological and localization transitions in non-Hermitian systems reveal new phenomena, e.g., the non-Hermitian skin effect and the absence of conventional bulk-boundary correspondence. The great majority of previous studies exclusively focus on non-Hermitian Hamiltonians, whose realization requires an a priori fine-tuned extended lattice to exhibit topological and localization transition phenomena. In this work, we show how the non-Hermitian localization phenomena can naturally emerge in the synthetic field moment space of zero-dimensional bosonic systems, e.g., in $\mathrm{anti}-\mathcal{PT}$- and $\mathcal{PT}-\mathrm{symmetric}$ quantum dimers. This offers an opportunity to simulate localization transitions in low-dimensional systems, without the need to construct complex arrays of, e.g., coupled cavities or waveguides. Indeed, the field moment equations of motion can describe an equivalent (quasi)particle moving in a one-dimensional (1D) synthetic lattice. This synthetic field moment space can exhibit nontrivial localization phenomena, such as non-Hermitian skin effect, induced by the presence of highly degenerate EPs. We demonstrate our findings on the example of an $\mathrm{anti}-\mathcal{PT}-\mathrm{symmetric}$ two-mode system, whose higher-order field moment eigenspace is emulated by a synthetic 1D non-Hermitian Hamiltonian having a Sylvester matrix shape. Our results can be directly verified in state-of-the-art optical setups, such as superconducting circuits and toroidal resonators, by measuring photon moments or correlation functions.

We develop a fundamental transfer-matrix formulation of the scattering of electromagnetic (EM) waves that incorporates the contribution of the evanescent waves and applies to general stationary linear media which need not be isotropic, homogenous, or passive. Unlike the traditional transfer matrices whose definition involves slicing the medium, the fundamental transfer matrix is a linear operator acting in an infinite-dimensional function space. It is given in terms of the evolution operator for a nonunitary quantum system and has the benefit of allowing for analytic calculations. In this respect it is the only available alternative to the standard Green's-function approaches to EM scattering. We use it to offer an exact solution of the outstanding EM scattering problem for an arbitrary finite collection of possibly anisotropic nonmagnetic point scatterers lying on a plane. In particular, we provide a comprehensive treatment of doublets consisting of pairs of isotropic point scatterers and study their spectral singularities. We show that identical and $\mathcal{P}\mathcal{T}$-symmetric doublets do not admit spectral singularities and cannot function as a laser unless the real part of their permittivity equals that of the vacuum. This restriction does not apply to doublets displaying anti-$\mathcal{P}\mathcal{T}$-symmetry. We determine the lasing threshold for a generic anti-$\mathcal{P}\mathcal{T}$-symmetric doublet and show that it possesses a continuous lasing spectrum.

Quantum state discrimination involves identifying a given state out of a set of possible states. When the states are mutually orthogonal, perfect state discrimination is always possible using a global measurement. In the case of multipartite systems when the parties are constrained to use multiple rounds of local operations and classical communication (LOCC), perfect state discrimination is often impossible even with the use of asymptotic LOCC, wherein an error is allowed but must vanish in the limit of an infinite number of rounds. Utilizing our recent results on asymptotic LOCC, we derive a lower bound on the error probability for LOCC discrimination of any given set of mutually orthogonal pure states. Informed by the insights gained from this lower bound, we are able to prove necessary conditions for perfect state discrimination by asymptotic LOCC. We then illustrate by example the power of these necessary conditions in significantly simplifying the determination of whether perfect discrimination of a given set of states can be accomplished arbitrarily closely using LOCC. The latter examples include a proof that perfect discrimination by asymptotic LOCC is impossible for any minimal unextendible product basis (UPB), where minimal means that for the given multipartite system no UPB with a smaller number of states can exist. We also give a simple proof that what has been called strong nonlocality without entanglement is considerably stronger than had previously been demonstrated.

Whenever a physical quantity becomes essential to the realization of useful tasks, it is desirable to define proper measures or monotones to quantify it. In quantum mechanics, coherence, entanglement, and Bell nonlocality are examples of such quantities. Given a quantum state $\varrho$ and a quantifier $\mathcal{E}\left(\varrho \right)$, both arbitrary, it is generally a hard task to determine $\mathcal{E}\left({\varrho }^{\otimes N}\right)$. However, if $\mathcal{E}$ turns out to be additive, we simply have $\mathcal{E}\left({\varrho }^{\otimes N}\right)=Ne$ with $e=\mathcal{E}\left(\varrho \right)$. In this paper we generalize this useful notion through the inner product $\mathcal{E}\left({\varrho }^{\otimes N}\right)=\vec{N}·\vec{e}$, where $\vec{e}=[\mathcal{E}\left({\varrho }^{\otimes i_1}\right),\mathcal{E}\left({\varrho }^{\otimes i_2}\right),...,\mathcal{E}\left({\varrho }^{\otimes i_q}\right)]$ is a vector whose $q$ entries are the figure of merit under study calculated for some numbers of copies smaller than $N$ ($1\le i_1<i_2<\cdots <i_q<N$) and $\vec{N}=(N_{i_1},N_{i_2},...,N_{i_q})$ is a string of numbers that depends only on $N$ and on the set of integers $\left\{i_j\right\}$. The (vector) linear dependence enables a full analytic treatment, and the determination of asymptotic results ($N\to \infty$), which may or may not be regular. We show that the one shot distillable entanglement of certain spherically symmetric states can be quantitatively approximated by such an augmented additivity.

We study the performance of an $N$-qubit $W$ superposition state composed of a $W$ state and its obverse in quantum metrology. Taking advantage of the general Ising-type Hamiltonian (including noninteracting and interacting operation), we analytically present the quantum Fisher information (QFI) of an $N$-qubit $W$ superposition state under different situations and then investigate its phase sensitivity. The results show that the phase sensitivity under noninteracting operation displays a crossover from the $W$ state to Greenberger-Horne-Zeilinger (GHZ) state, where it is same as $W$ state in the few-qubit case $(N\le 6)$ but asymptotically equal to the GHZ state for large-qubit cases $(N\gg 1)$. Interestingly, the 4-qubit $W$ superposition state is found to have the same sensitivity as the 4-qubit GHZ state. And the optimal measurement protocols are provided for ideal metrology. Under the phase-amplitude damping channel, the phase sensitivity of the $W$ superposition state (except for $N=3$) is ultimately decreased to the standard quantum limit, while it turns worse in a depolarizing channel. Finally, the tunable phase sensitivity under interacting operation is studied, and the general Heisenberg limit is surpassed with the increasing interaction strength $\gamma$. Meanwhile, a plateau of QFI and phase sensitivity is found for all large-qubit $W$ superposition states, which is similar to the study of the GHZ state and again verifies the common feature of GHZ-type states in quantum metrology.

In 2016, Winter and Yang [A. Winter and D. Yang, Phys. Rev. Lett. 116, 120404 (2016)] provided an operational meaning to relative entropy of coherence and coherence of formation by introducing coherence distillation and dilation protocols in an asymptotic setup. Here we have provided relative entropy of coherence [via incoherent operations (IO)] and coherence of formation (via IO) and quantum incoherent relative entropy [via local quantum incoherent operations with classical communications (LQICC)] as a measure using the concept of a catalyst. We have proved an existential correspondence between asymptotic and catalytic state transformation using IO, local incoherent operations with classical communications, and LQICC. We have also discussed two very important protocols, assisted distillation and quantum incoherent state merging using a catalyst. Monotone properties of relative entropy of coherence, coherence of formation, and quantum incoherent relative entropy under the catalytic transformation are also discussed here.

Nuclear spins in quantum dots are promising candidates for fast and scalable quantum memory. By utilizing the hyperfine interaction between the central electron and its surrounding nuclei, quantum information can be transferred to the collective state of the nuclei and stored for a long time. However, nuclear spin fluctuations in a partially polarized nuclear bath degrade the quantum memory fidelity. Here, we introduce a noise-resistant protocol to realize fast and high-fidelity quantum memory through Hamiltonian engineering. With analytics and numerics, we show that a high-fidelity quantum state transfer between the electron and the nuclear spins is achievable at relatively low nuclear polarizations, due to the strong suppression of nuclear spin noises. For a realistic quantum dot with ${10}^4$ nuclear spins, a fidelity surpassing 80% is possible at a polarization as low as 30%. Our approach reduces the demand for high nuclear polarization, making experimentally realizing quantum memory in quantum dots more feasible.

In this paper we study the role of parasitic interactions and microwave crosstalk in a system of two superconducting artificial atoms interacting via a single-mode coplanar waveguide. Through a general description of the effective dynamics of the atoms, beyond the two-level approximation, we show that the atom selectivity (ability to individually address an atom) is only dependent on the resultant phasor associated to the drives used to control the system. We then exploit the benefits of such a drive-dependent selectivity to describe how the coherent population inversion occurs in the atoms simultaneously, with no interference of residual atom-atom interaction. In this scenario the parasitic interaction works as a resource to fast and high fidelity control, as it gives rise to a new regime of frequencies for the atoms able to suppress effective atom-atom coupling (idling point). To end, we show how an entangling $\mathrm{iSWAP}$ gate is implemented with fidelity higher than $99\%$, even in the presence of parasitic interactions. More than that, we argue that the existence of this interaction can be helpful to speed up the gate performance. Our results open prospects to an outlook on the real role of such “undesired” effects in a system of superconducting artificial atoms.

We have performed a kinematically complete experiment for state-selective double-electron capture occurring in 15-keV/u ${\mathrm{C}}^{4+}$ $+$ He collisions by means of cold-target recoil-ion momentum spectroscopy. It was shown that capture into ground and low excited states of the ${\mathrm{C}}^{2+}$ ions is overwhelmingly dominant. Besides, a small fraction of autoionization decays from doubly excited states of symmetric as well as asymmetric electron configurations following endothermic double-electron capture were clearly observed. Emphasis was given to the population mechanisms of the different electron configurations. Our analysis indicates that electron-electron correlation effects may play a major role in the double-electron capture process. In addition, the large transverse recoil-ion momentum of symmetric configurations as compared to asymmetric configurations for the doubly excited autoionizing states may be attributed to the different number of steps involved in the primary capture process, with the former likely produced by a two-step mechanism and the latter by a one-step mechanism.

Accurate spectroscopy of molecular hydrogen isotopologues is used for testing quantum electrodynamics and searching for physics beyond the standard model. Recent measurements of energies of rovibrational resonances in the ground electronic state have reached a level of uncertainty lower than the magnitude of the hyperfine splitting. The underlying hyperfine components of the resonance clearly perturb sub-Doppler saturation spectra. The extent to which hyperfine structure influences the Doppler-limited spectra is not fully understood, as there are two contradicting experimental works that show either a 350 kHz shift or lack of any deviation from the central frequency of the resonance in the HD molecule. Here, we address this problem theoretically. Using the spherical tensor approach, we prove that the barycenter of all hyperfine-resolved spectra corresponds to the unperturbed transition frequency (the first moment of the hyperfine-resolved spectra vanishes). This property is directly transferred to Doppler-limited spectra: we show that there is no detectable shift due to the hyperfine structure unless the ratio of the Doppler width to the root-mean-square hyperfine splitting is less than 50.

The propagation of a photon in an atomic medium can be seen as a Lévy-flight random walk where the probability distribution $P\left(z\right)$ for the photon step length $z$ scales with $z^{-(\alpha +1)}$, with $0<\alpha <2$. In atomic vapors, previous work reported the value of $\alpha$ obtained from direct measurement of $P\left(z\right)$ and also from the dependence of transmission on sample opacity, both for Doppler and Lorentz profiles. In this work, we report the measurement of $\alpha$ in a Cs cell from the scaling of transmission with starting point, i.e., the average penetration depth of the photon in the medium before the first scattering event. We show that the parameter $\alpha$ depends on the size of the system and on the probability that an atom suffers a collision before spontaneous emission. The measured $\alpha$ parameter corresponds to the expectation value for $P(z=L)$, with $L$ the size of the system, which is consistent with the so-called single-big-jump principle that states that a single jump rules the transport.

Quantum oscillators in Gaussian states are often characterized by average occupation numbers that refer to a basis of eigenstates of the noninteracting oscillator Hamiltonian. We argue that quantum state purity is a more appropriate characteristic of such states, which can be applied to oscillators of any dimensionality. For a one-dimensional oscillator, the state purity is directly related to a thermal occupation number defined with respect to the number state basis in which the oscillator's quantum state is thermal. Thus, it naturally introduces a more versatile definition of an average occupation number. We study optomechanical sideband cooling of one- and two-dimensional mechanical oscillators in particular, and derive exact analytical expressions for the maximal mechanical state purity achievable in the quantum backaction limit. In the case of a one-dimensional oscillator, we show that the thermal occupation number related to purity can be well approximated by the average phonon number in the weak-coupling regime, but that the two differ in the regime of ultrastrong optomechanical coupling or in cases where the oscillator's resonance frequency is strongly renormalized.

It is a nonlinear and nonperturbative optical phenomenon that high-order harmonic generation (HHG) can be produced by the interaction of intense laser pulses with liquid targets. The theoretical studies on HHG in liquids based on full dimensional simulations meet the difficulty of very low computational efficiency. Here, we develop an efficient numerical method based on the statistical mechanics in two-dimensional space, which reproduces the experimental HHG measurements very well. We also study the HHG in bicircularly polarized $1\omega$ $+$ $3\omega$ laser fields with the same field strength. It is found that near-circularly-polarized harmonics with different ellipticities can be generated in the counterrotating driving lasers. The cutoff energy of HHG in counter- and corotating driving lasers demonstrates a similar dependence of laser field strength and wavelength as that in the case of a linearly polarized driving laser field. This work paves the way for controlling the ultrafast electron dynamics in liquids by manipulating the laser fields.

We analyze the dynamics of quantum beats in a system of two V-type three-level atoms coupled to a waveguide. We show that quantum beats can be collectively enhanced or suppressed, akin to Dicke super- and subradiance, depending on the interatomic separation and the initial correlations between the atoms. In particular, the interference properties of the collective beats are determined by the distance between the atoms modulo the beat wavelength. We study the collective atomic and field dynamics, illustrating a crossover from a Markovian to a non-Markovian regime as the atomic separation becomes sufficiently large to bring memory effects of the electromagnetic environment into consideration. In such a non-Markovian regime, collective quantum beats can be enhanced beyond the Markovian limit as a result of retardation effects. Our results demonstrate the rich interplay between multilevel and multiatom quantum interference effects arising in a system of distant quantum emitters.