Eigenenergy Spectrum Research Articles

SHORYUKEN: An open-source software package for calculating nonlocal exchange interactions in nanowires

We present the open-source software package, SHORYUKEN (Streamlined High-level Operations in Real-space to Yield, Understand, and Keep Exchange in Nanowires), for calculating nonlocal exchange interactions in nanowires with arbitrary geometries, sizes, doping densities, and compositions. In addition to enabling new calculations of nonlocal exchange, the SHORYUKEN software package is a significant enhancement of our previous HADOKEN code and includes new algorithmic improvements as well as an improved treatment of surface states for nanowires with intrinsic polarization. Our calculations show that the inclusion of nonlocal exchange can have significant effects on the eigenenergy spectrum, number of occupied states, and distribution of electrons within these nanosystems. The SHORYUKEN software package is the first open-source code for calculating nonlocal exchange to predict electron gas formation in nanowire systems with arbitrary cross-sectional geometries. Program summaryProgram Title: SHORYUKENCPC Library link to program files:https://doi.org/10.17632/f77p84pbcv.1Licensing provisions: GNU General Public License 3Programming language: MATLABNature of problem: The SHORYUKEN code calculates nonlocal exchange interactions of electrons in nanowires by solving modified nonlocal exchange and Poisson-like equations self-consistently on a finite element grid. The software package is capable of performing calculations for core-multishell nanowires with arbitrary cross-sectional shapes.Solution method: iterative solution of the Schrödinger-Poisson equations with nonlocal exchange using finite element methods and sparse matrix linear algebra

Exceptional Entanglement and Quantum Sensing with a Parity‐Time‐Symmetric Two‐Qubit System

AbstractParity‐time (PT) symmetric systems with gain‐loss balanced structures can have entirely real eigenenergy spectra despite their non‐Hermitian nature, leading to peculiar discoveries such as single‐mode lasers, wireless power transfer, and non‐reciprocal light propagation. Recently, the study of PT‐symmetry has extended to the quantum realm, inspiring a search for PT‐symmetric quantum effects as well as their unique applications. Here, quantum entanglement and sensing with a PT‐symmetric system of two qubits are studied with Ising‐type interaction. It is shown that exceptional points (EPs) can induce exceptional entanglement phenomena such as collapse‐revival and steady‐state entanglement on the two sides of EPs. The entanglement in the PT‐symmetric system is also found to be generated more quickly than that in the Hermitian counterpart. In addition, a scheme for realizing EP‐enhanced quantum sensing is proposed by calculating the quantum Fisher information to estimate the parameters of the system. The work provides new insights into EP‐engineered quantum effects and can benefit a wide range of applications based on non‐Hermitian quantum devices.

Terminal-coupling induced critical eigenspectrum transition in closed non-Hermitian loops

A hallmark feature of non-Hermitian (NH) systems is the non-Hermitian skin effect (NHSE), in which the eigenenergy spectra of the system under open boundary conditions (OBC) and periodic boundary conditions (PBC) differ markedly from each other. In particular, the critical NHSE occurs in systems consisting of multiple non-Hermitian chains coupled in parallel where even an infinitesimally small inter-chain coupling can cause the thermodynamic-limit eigenenergy spectrum of the system to deviate significantly from the OBC spectra of the individual component chains. We overturn the conventional wisdom that multiple chains are required for such critical transitions by showing that such a critical effect can also be induced in a single finite-length non-Hermitian chain where its two ends are connected together by a weak terminal coupling to form a closed loop. An infinitesimally small terminal coupling can induce the thermodynamic-limit energy spectrum of the closed loop to switch from the OBC to the PBC spectrum of the chain. Similar to the critical NHSE, this switch occurs abruptly when the chain length exceeds a critical size limit. We explain analytically the underlying origin of the effect in a Hatano–Nelson chain system, and demonstrate its generality in more complex one-dimensional non-Hermitian chains. Our findings illustrate the generality of critical size-dependent effects in finite NH systems that arise from the interplay between the interfacial boundary conditions and the influence of edge localization.

Photon blockade with a trapped Λ-type three-level atom in asymmetrical cavity.

We propose a scheme to manipulate strong and nonreciprocal photon blockades in asymmetrical Fabry-Perot cavity with a Λ-type three-level atom. Utilizing the mechanisms of both conventional and unconventional blockade, the strong photon blockade is achieved by the anharmonic eigenenergy spectrum brought by Λ-type atom and the destructive quantum interference effect induced by a microwave field. By optimizing the system parameters, the manipulation of strong photon blockade over a wide range of cavity detuning can be realized. Using spatial symmetry breaking introduced by the asymmetry of cavity, the direction-dependent nonreciprocal photon blockade can be achieved, and the nonreciprocity can reach the maximum at optimal cavity detuning. In particular, manipulating the occurring position of nonreciprocal photon blockade can be implemented by simply adjusting the cavity detuning. Our scheme provides feasible access for generating high-quality nonreciprocal single-photon sources.

Floquet space exploration for the dual-dressing of a qubit

The application of a periodic nonresonant drive to a system allows the Floquet engineering of effective fields described by a broad class of quantum simulated Hamiltonians. The Floquet evolution is based on two different elements. The first one is a time-independent or stroboscopic evolution with an effective Hamiltonian corresponding to the quantum simulation target. The second element is the time evolution at the frequencies of the nonresonant driving and of its harmonics, denoted as micromotion. We examine experimentally and theoretically the harmonic dual-dressing Floquet engineering of a cold atomic two-level sample. Our focus is the dressing operation with small bare energies and large Rabi frequencies, where frequencies and amplitudes of the stroboscopic/micromotion time evolutions are comparable. At the kHz range of our dressed atom oscillations, we probe directly both the stroboscopic and micromotion components of the qubit global time evolution. We develop ad-hoc monitoring tools of the Floquet space evolution. The direct record of the time evolution following a pulsed excitation demonstrates the interplay between the two components of the spin precession in the Floquet space. From the resonant pumping of the dressed system at its evolution frequencies, Floquet eigenenergy spectra up to the fifth order harmonic of the dressing frequency are precisely measured as function of dressing parameters. Dirac points of the Floquet eigenenergies are identified and, correspondingly, a jump in the dynamical phase shift is measured. The stroboscopic Hamiltonian eigenfrequencies are measured also from the probe of the micromotion sidebands.These monitoring tools are appropriate for quantum simulation/computation investigations. Our results evidence that the stroboscopic phase shift of the qubit wavefunction contains an additional information that opens new simulation directions.

Realizing tight-binding Hamiltonians using site-controlled coupled cavity arrays

Analog quantum simulators rely on programmable and scalable quantum devices to emulate Hamiltonians describing various physical phenomenon. Photonic coupled cavity arrays are a promising alternative platform for realizing such simulators, due to their potential for scalability, small size, and high-temperature operability. However, programmability and nonlinearity in photonic cavities remain outstanding challenges. Here, using a silicon photonic coupled cavity array made up of 8 high quality factor (Q up to, sim 7.1times {10}^{4}) resonators and equipped with specially designed thermo-optic island heaters for independent control of cavities, we demonstrate a programmable photonic cavity array in the telecom regime, implementing tight-binding Hamiltonians with access to the full eigenenergy spectrum. We report a sim 50% reduction in the thermal crosstalk between neighboring sites of the cavity array compared to traditional heaters, and then present a control scheme to program the cavity array to a given tight-binding Hamiltonian. The ability to independently program high-Q photonic cavities, along with the compatibility of silicon photonics to high volume manufacturing opens new opportunities for scalable quantum simulation using telecom regime infrared photons.

Simultaneous nonreciprocal conventional photon blockades of two independent optical modes by a two-level system

We propose a scheme to achieve nonreciprocal conventional photon blockades simultaneously in two independent optical modes, which are connected by a two-level system. In the case that only one optical mode is weakly driven, we find that strong nonreciprocal photon blockades of both optical modes can be observed. We show that, for both optical modes, the single-photon blockades happens by driving the nonlinear device from one side, while photon-induced tunneling appears when driving the system from the other side, which is attributed to the anharmonic eigenenergy spectrum constructed by resonantly coupling to a two-level system. According to photon resonance transition processes under different driving directions, the four optimal Fizeau-Sagnac shifts can be obtained to generate perfect nonreciprocal conventional photon blockades of both optical modes. Our study opens an avenue to simultaneously manipulate multiple nonreciprocal single-photon devices and may have potential applications in chiral quantum information processing.

Simultaneously enhanced photon blockades in two microwave cavities via driving a giant atom

We propose a scheme to enhance photon blockades simultaneously in two microwave cavities connected by a giant atom. In the case that only one cavity is weakly driven, we observe that the enhanced photon blockades occur in both cavities at the same time, which is attributed to the anharmonic eigenenergy spectrum constructed by the resonantly coupled giant atom. When the cavity and the atom are simultaneously driven, the stronger photon blockades in two cavities can be successfully achieved by the destructive quantum interference of two-photon excitation. Interestingly, we find that high single-photon occupations can be obtained in both cases. Moreover, we give the optimal conditions for conventional and unconventional photon blockades through analytical calculations, which are in good agreement with numerical results. Our scheme opens a prospective path to achieve simultaneous photon blockades in two indirectly coupled cavities, and provides a promising method to generate the high-quality and brightness single photon source.

Manifold formation and crossings of ultracold lattice spinor atoms in the intermediate interaction regime

Ultracold spinor atoms in the weak and strong interaction regimes have been extensively investigated, while the behavior in the intermediate regime is less understood. We numerically investigate one-dimensional ultracold spinor atomic ensembles of finite size in the intermediate interaction regime and reveal the evolution of the eigenstates from the strong to the intermediate regime. In the strong interaction regime, it is well known that the eigenstates can be categorized into different manifolds, and the categorization is protected by the energy gaps between manifolds. In the intermediate interaction regime, it is found that the eigenenergy spectrum becomes gapless, while categorization of the eigenstates is still preserved even without the protection from the intermanifold gaps. The categorization in the intermediate regime is found due to the minigap induced by the finite-size effect, which prevents the intermanifold coupling. The gap vanishing in the spectrum induces both direct and avoided crossings between close-lying manifolds, of which the combined symmetries determine the type of the crossings. A modified $t\text{\ensuremath{-}}J$ model is derived to describe the low-lying eigenstates in the intermediate regime, which can capture the formation and crossings of the manifolds. State preparation through avoided crossings is also investigated.

Spectral collapse in mixed Rabi model

In this paper we have conducted a simple variational study of the ground state of the mixed Rabi model, namely the variant of the Rabi model with both one-photon and two-photon couplings of light-matter interaction. We have shown how the spectral collapse occurs beyond the critical value of the two-photon coupling. Our analysis also indicates that the upper bound of the ground-state energy approaches negative infinity as the two-photon coupling strength increases towards the critical value. This special feature is clearly generated by the one-photon coupling and disappears in the absence of the one-photon process. Likewise, we have investigated the eigenenergy spectrum of the mixed Rabi model near the critical coupling. It is found that the energy spectrum essentially consists of a continuum and some discrete energy levels below it. Indeed, it is reminiscent of the incomplete spectral collapse of the two-photon Rabi model.

Enhanced Phonon Blockade in a Weakly Coupled Hybrid System via Mechanical Parametric Amplification

We propose how to achieve strong phonon blockade (PB) in a hybrid spin-mechanical system in the weak-coupling regime. We demonstrate the implementation of magnetically induced two-phonon interactions between a mechanical cantilever resonator and an embedded nitrogen-vacancy center, which, when combined with parametric amplification of the mechanical motion, produces significantly enlarged anharmonicity in the eigenenergy spectrum. In the weak-driving regime, we show that strong PB appears in the hybrid system along with a large mean phonon number, even in the presence of strong mechanical dissipation. We also show flexible tunability of phonon statistics by controlling the strength of mechanical parametric amplification. Our work opens up prospects for the implementation of an efficient single-phonon source, with potential applications in quantum phononics and phononic quantum networks.

Photon blockade in a cavity–atom optomechanical system

We study the single-photon blockade (1PB), two-photon blockade (2PB), and photon-induced tunneling (PIT) effects in a cavity–atom optomechanical system in which a two-level atom is coupled to a single-model cavity field via a two-photon interaction. By analyzing the eigenenergy spectrum of the system, we obtain a perfect 1PB with a high occupancy probability of single-photon excitation, which means that a high-quality and efficient single-photon source can be generated. However, PIT often occurs in many cases when we consider 2PB in analogy to 1PB. In addition, we find that a 2PB region will present in the optomechanical system, which can be proved by calculating the correlation function of the model analytically.

Retrieval of photon blockade effect in the dispersive Jaynes-Cummings model

We propose a reliable scheme to recover the conventional photon blockade effect in the dispersive Jaynes-Cummings model, which describes a two-level atom coupled to a single-mode cavity field in the large-detuning regime. This is achieved by introducing a transversal driving to the atom and then photonic nonlinearity is obtained. The eigenenergy spectrum of the system is derived analytically and the photon blockade effect is confirmed by numerically calculating the photon-number distributions and equal-time second-order correlation function of the cavity field in the presence of system dissipations. We find that the conventional photon blockade effect can be recovered at proper atomic and cavity-field drivings. This work will provide a method to generate the conventional photon blockade effect in the dispersively coupled quantum optical systems.

Suppression of non-Hermitian skin effect via Aharonov-Bohm cage

The application of energy band theory in optics provides an effective approach to modulating the flow of light. The recent discovery of non-Hermitian skin effect promotes the development of traditional energy band theory, which further enables an alternative way to realize light localization and unidirectional propagation. However, how to effectively generate and steer the non-Hermitian skin effect is still an important topic, especially in integrated optical systems. Here, we investigate the non-Hermitian skin effect in quasi-one-dimensional rhombic optical lattice with synthetic gauge potential. By calculating the eigenenergy spectra, spectral winding number, and wave dynamics, the gauge potential can be utilized to effectively tune the localization strength of skin modes. In particular, the skin effect is completely suppressed when the gauge potential in each plaquette is equal to π, while the flat-band localization caused by Aharonov-Bohm caging effect is dominant. By utilizing the indirectly coupled micro ring resonator array, the gauge potential and asymmetric coupling can be generated at the same time, which provides a potential experimental scheme to explore the competition between Aharonov-Bohm cage and skin effect. The present study provides an alternative way to steer the skin effect, which offers an approach to achieving the on-chip non-magnetic unidirectional optical devices.

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice* *Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0300600 and 2016YFA0302104), the National Natural Science Foundation of China (Grant Nos. 12074410, 12047502, 11934015, 11947301, and 11774397), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB33000000), and the Fellowship of

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials. We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones, which implies that the system has mobility edges. The localization transition is accompanied by the symmetry breaking transition. While if the non-Hermitian quasiperiodic disorder is staggered, we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis. Interestingly, some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters. The reentrant localization transitions are associated with the intermediate phases hosting mobility edges. Besides, we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives. More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum, inverse participation ratio, and normalized participation ratio.

Spectral collapse in anisotropic two-photon Rabi model

In this communication, based upon a squeezed-state trial wave function, we have performed a simple variational study of the spectral collapse in the anisotropic two-photon Rabi model. Our analysis indicates that the light-matter interaction and the spin-flipping (together with the anisotropy) effectively constitute two competing impacts upon the radiation mode. Whilst the former tries to decrease the radiation mode frequency, the latter may counteract or reinforce it. The light-matter interaction appears to dominate the frequency modulation as its coupling strengths go beyond the critical values, leading to the emergence of the spectral collapse. However, at the critical couplings the dominance of the light-matter interaction is not complete, and incomplete spectral collapse appears. Accordingly, at the critical couplings the eigenenergy spectrum comprises both a set of discrete energy levels and a continuous energy spectrum. The discrete eigenenergy spectrum can be derived via a simple one-to-one mapping to the bound state problem of a particle of variable effective mass in a finite potential well, and the number of bound states available is determined by the energy difference between the two atomic levels. Each of these eigenenergies has a twofold degeneracy corresponding to the spin degree of freedom.

Exact eigenenergies of a model of vibronically coupled electron transfer reactions.

We present the first exact solution to the time-independent Schrödinger equation of a model Hamiltonian consisting of a vibrational mode coupled to three electronic states. This Hamiltonian serves as a generic model for photo-induced electronic transfer reactions. The solution is non-perturbative and can be applied to ET reactions with weak and strong electronic and vibrational coupling strengths. This work suggests a new direction towards understanding the vibronic effects in ET dynamics beyond the non-adiabatic limit and Condon approximation.

Coherent single-spin electron resonance spectroscopy manifested at an exceptional-point singularity in doped polyacetylene

Spin-dependent charge-transfer decay in an alkali atom-doped polyacetylene is studied in terms of the complex spectral analysis, revealing the single-spin Zeeman splitting influenced by the spin-orbit interaction. A non-Hermitian effective Hamiltonian has been derived from the total system Hermitian Hamiltonian using the Brillouin-Wigner-Feshbach projection method where the microscopic spin-dependent dissipation effect is correctly incorporated in the energy-dependent self-energy. Since the present method maintains the dynamical and chiral symmetries of the total system, we discovered two types of exceptional point (EP) singularities: The EP surface and the EP ring are attributed to the dynamical and chiral symmetry breaking, respectively. We reveal that the coherent single-spin electron resonance (SSESR) spectrum reflects the complex eigenenergy spectrum of the system. We formulate the SSESR spectrum in terms of the non-linear-response function in the Liouville-space pathway approach where we have constructed the Liouville-space basis using the complex eigenstates of the total Hamiltonian. We calculate the one-dimensional Fourier transform (1DFT) and two-dimensional Fourier transform (2DFT) SSESR spectra reflecting the spin-relaxation dynamics at the donor site. Whereas the 1DFT SSESR spectrum reflects the complex eigenenergy spectrum, the 2DFT gives detailed information about the quantum coherence in the spin-relaxation dynamics as a cross correlation between the two frequencies. We reveal a giant response in the coherent SSESR around the EP ring singularity due to the vanishing normalization factors at the EP ring and the resonance effect. We show this giant response is even more heavily pronounced in the 2DFT spectrum than in the 1DFT spectrum, which illustrates that the 2DFT SSESR can become a useful tool to observe the single-spin response of a molecule.

Spectral collapse in two-mode two-photon Rabi model

We have investigated the eigenenergy spectrum of the two-mode two-photon Rabi model at the critical coupling, particularly the special feature “spectral collapse”. The eigenenergy spectrum is found to consist of both a set of discrete energy levels and a continuous energy spectrum. Each of these eigenenergies has a two-fold degeneracy corresponding to the spin degree of freedom. The discrete eigenenergy spectrum has a one-to-one mapping with that of a particle in an isotropic two-dimensional ”Lorentzian function” potential well, and the continuous energy spectrum can be derived from the scattering problem associated with an isotropic two-dimensional potential barrier. The number of bound states available at the critical coupling is determined by the energy difference between the two atomic levels so that the extent of the “spectral collapse” can be monitored straightforwardly.

Spectral collapse in multiqubit two-photon Rabi model

We have shown that the smallest possible singel-qubit critical coupling strength of the N-qubit two-photon Rabi model is only 1/N times that of the two-photon Rabi model. The spectral collapse can thus occur at a more attainable value of the critical coupling. For both of the two-qubit and three-qubit cases, we have also rigorously demonstrated that at the critical coupling the system not only has a set of discrete eigenenergies but also a continuous energy spectrum. The discrete eigenenergy spectrum can be derived via a simple one-to-one mapping to the bound state problem of a particle of variable effective mass in the presence of a finite potential well and a nonlocal potential. The energy difference of each qubit, which specifies both the depth of the finite potential well and the strength of the nonlocal potential, determines the number of bound states available, implying that the extent of the incomplete spectral collapse can be monitored in a straightforward manner.