We examine the Stark effect (the second-order shift in the energy spectrum due to an external constant force) for two 1-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z>0 and V(z) infinite for z<0) and the symmetric linear potential (given by V(z) = F|z|). We show how straightforward use of the most obvious properties of the Airy function solutions and simple Taylor expansions give closed form results for the Stark shifts in both systems. These exact results are then compared to other approximation techniques, such as perturbation theory and WKB methods. These expressions add to the small number of closed-form descriptions available for the Stark effect in model quantum mechanical systems.
In this paper we investigate the completeness of the Stark resonant eigenstates for a particle in a square-well potential. We find that the resonant state expansions for target functions converge inside the potential well and that the existence of this convergence does not depend on the depth of the potential well. By analyzing the asymptotic form of the terms in these expansions we prove some results on the relation between smoothness of target functions and the rate of convergence of the corresponding resonant state expansion.
In this work we reproduce the phenomenology of the electromagnetically induced transparency and dynamic Stark effect in a dissipative system composed by two coupled bosonic fields under linear and nonlinear amplification process. Such a system can be used as a quantum switch in networks of oscillators.
We show that, under certain conditions, the micromaser can act as an effective source of highly correlated atoms. It is possible to create an extended robust entanglement between two successive, initially unentangled atoms passing through a cavity filled with with a nonlinear medium taking into consideration a slight level shift. Information is transfered from the cavity to the atoms in order to build up entanglement. The scheme has an advantage over conventional creation of entanglement if the two atoms (qubits) are so far apart that a direct interaction is difficult to achieve. The interacti…
In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier-Stark problem without any approximation. The suggested method is very efficient fr…
The resonance spectrum of a tilted periodic quantum system for a bichromatic periodic potential is investigated. For such a bichromatic Wannier-Stark system exceptional points, degeneracies of the spectrum, can be localized in parameter space by means of an efficient method for computing resonances. Berry phases and Petermann factors are analyzed. Finally the influence of a nonlinearity of the Gross-Pitaevskii type on the resonance crossing scenario is briefly discussed.
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found.
Lifetime limited optical excitation lines of single nitrogen vacancy (NV) defect centers in diamond have been observed at liquid helium temperature. They display unprecedented spectral stability over many seconds and excitation cycles. Spectral tuning of the spin selective optical resonances was performed via the application of an external electric field (i.e. the Stark shift). A rich variety of Stark shifts were observed including linear as well as quadratic components. The ability to tune the excitation lines of single NV centers has potential applications in quantum information processing.
We consider the dipole transitions and the linear and quadratic Stark effect in the MICZ-Kepler system interpreting as a charge-dyon system. We show, that while the linear Stark effect in the ground state is proportional to azimuth quantum number(and to the sign of monopole number), the quadratic Stark effect in the ground state is independent on the signs of azimuth and monopole numbers.
Quantum memories for optical and microwave photons provide key functionalities in quantum processing and communications. Here we propose a protocol well adapted to solid state ensemble based memories coupled to cavities. It is called Stark Echo Modulation Memory (SEMM), and allows large storage bandwidths and low noise. This is achieved in a echo like sequence combined with phase shifts induced by small electric fields through the linear Stark effect. We investigated the protocol for rare earth nuclear spins and found a high suppression of unwanted collective emissions that is compatible with …
We present measurements of the linear Stark effect on the $^{4}$I$_{15/2} \to$ $^{4}$I$_{13/2}$ transition in an Er$^{3+}$-doped proton-exchanged LiNbO$_{3}$ crystalline waveguide and an Er$^{3+}$-doped silicate fiber. The measurements were made using spectral hole burning techniques at temperatures below 4 K. We measured an effective Stark coefficient $(Δμ_{e}χ)/(h)=25\pm1$kHz/Vcm$^{-1}$ in the crystalline waveguide and $(\bar{Δμ_{e}}χ)/(h)=15\pm1$kHz/Vcm$^{-1}$ in the silicate fiber. These results confirm the potential of Erbium doped waveguides for quantum state storage based on controlled …
We analyse the geometric phase due to the Stark shift in a system composed of a bosonic field, driven by time-dependent linear amplification, interacting dispersively with a two-level (fermionic) system. We show that a geometric phase factor in the joint state of the system, which depends on the fermionic state (resulting form the Stark shift), is introduced by the amplification process. A clear geometrical interpretation of this phenomenon is provided. We also show how to measure this effect in an interferometric experiment and to generate geometric "Schrodinger cat"-like states. Finally, con…
Various quantum phase transitions in the anisotropic Rabi-Stark model with both the nonlinear Stark coupling and the linear dipole coupling between a two-level system and a single-mode cavity are studied in this work. The first-order quantum phase transitions are detected by the level crossing of the ground-state and the first-excited state with the help of the pole structure of the transcendental functions derived by the Bogoliubov operators approach. As the nonlinear Stark coupling is the same as the cavity frequency, this model can be solved by mapping to an effective quantum oscillator. Al…
We treat the eigenvalue problem posed by self-similar potentials, i.e. homogeneous functions under a particular affine transformation, by means of symmetry techniques. We find that the eigenfunctions of such problems are localized, even when the potential does not rise to infinity in every direction. It is shown that the logarithm of the energy displays levels contained in families that are analogous to Wannier-Stark ladders. The position of each ladder is proved to be determined by the specific details of the potential and not by its transformation properties. This is done by direct computati…
We propose a technique to prepare coherent superpositions of two nondegenerate quantum states in a three-state ladder system, driven by two simultaneous fields near resonance with an intermediate state. The technique, of potential application to enhancement of nonlinear processes, uses adiabatic passage assisted by dynamic Stark shifts induced by a third laser field. The method offers significant advantages over alternative techniques: (ı) it does not require laser pulses of specific shape and duration and (\ii) it requires less intense fields than schemes based on two-photon excitation with n…
We propose a theoretical scheme to achieve strong photon blockade via a single atom in cavity. By utilizing optical Stark shift, the dressed-state splitting between higher and lower branches is enhanced, which results in significant increasing for lower (higher) branch and decreasing for higher (lower) branch at the negative (positive) Stark shift, and dominates the time-evolution of photon number oscillations as well. Furthermore, the two-photon excitation is suppressed via quantum interference under optimal phase and Rabi frequency of an external microwave field. It is shown that the interpl…
The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling are present on an equal footing, are studied within the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived in a compact way, much simpler than previous ones obtained in the Bargmann representation. The zeros of transcendental functions reproduce completely the regular spectra. In terms of the explicit pole structure of these functions, two kinds of exceptional eigenvalues are obtained and distinguished in a transparent manner. Very interestin…
The dynamic Stark shift of a high-lying atom in a system of Bose Einstein condensation (BEC) of photons is discussed within the framework of nonrelativistic quantum electrodynamics (QED) theory. It is found that the Stark shift of an atom in BEC of photons is modified by a temperature dependent factor, compared to that in a normal two-dimensional photonic fluid. In photonic BEC, the value of Stark shift is always greater than that in two-dimensional free space. Physical origin of the phenomenon is presented and potential application is also discussed.
Recent numerical and experimental works have revealed a disorder-free many-body localization (MBL) in an interacting system subjecting to a linear potential, known as the Stark MBL. The conventional MBL, induced by disorder, has been widely studied by using quantum simulations based on superconducting circuits. Here, we consider the Stark MBL in two types of superconducting circuits, i.e., the 1D array of superconducting qubits, and the circuit where non-local interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highl…
We study the energy spectrum of atoms trapped in a vertical 1D optical lattice in close proximity to a reflective surface. We propose an effective model to describe the interaction between the atoms and the surface at any distance. Our model includes the long-range Casimir-Polder potential together with a short-range Lennard-Jones potential, which are considered non-perturbatively with respect to the optical lattice potential. We find an intricate energy spectrum which contains a pair of loosely-bound states localized close to the surface in addition to a surface-modified Wannier-Stark ladder …
In this paper we show that in the semicassical regime of periodic potential large enough, the Stark-Wannier ladders become a dense energy spectrum because of a cascade of bifurcations while increasing the ratio between the effective nonlinearity strength and the tilt of the external field; this fact is associated to a transition from regular to quantum chaotic dynamics. The sequence of bifurcation points is explicitly given.
The linear Stark effect in the MIC-Kepler problem describing the interaction of charged particle with Dirac's dyon is considered. It is shown that constant homogeneous electric field completely removes the degeneracy of the energy levels on azimuth quantum number
We report the use of novel, capacitively terminated coplanar waveguide (CPW) resonators to measure the quadratic Stark shift of phosphorus donor qubits in Si. We confirm that valley repopulation leads to an anisotropic spin-orbit Stark shift depending on electric and magnetic field orientations relative to the Si crystal. By measuring the linear Stark effect, we estimate the effective electric field due to strain in our samples. We show that in the presence of this strain, electric-field sources of decoherence can be non-negligible. Using our measured values for the Stark shift, we predict mag…
The phenomenon of Many-Body Stark Localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well known many body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches poissonian value as characteristic for localized situations but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may…
We investigated how the presence of an additional lattice potential, driven by a harmonic noise process, changes the transition rate from the ground band to the first excited band in a Wannier-Stark system. Alongside numerical simulations, we present two models that capture the essential features of the dynamics. The first model uses a noise-driven Landau-Zener approximation and describes the short time evolution of the full system very well. The second model assumes that the noise process' correlation time is much larger than the internal timescale of the system, yet it allows for good estima…
We present experimental observations of a non-resonant dynamic Stark shift in strongly coupled microcavity quantum well exciton-polaritons - a system which provides a rich variety of solid-state collective phenomena. The Stark effect is demonstrated in a GaAs/AlGaAs system at 10K by femtosecond pump-probe measurements, with the blue shift approaching the meV scale for a pump fluence of 2 mJcm^-2 and 50 meV red detuning, in good agreement with theory. The energy level structure of the strongly coupled polariton Rabi-doublet remains unaffected by the blue shift. The demonstrated effect should al…
We show how to compute the optical functions of Wide Parabolic Quantum Wells (WPQWs) exposed to uniform electric F applied in the growth direction, in the excitonic energy region. The effect of the coherence between the electron-hole pair and the electromagnetic field of the propagating wave including the electron-hole screened Coulomb potential is adopted, and the valence band structure is taken into account in the cylindrical approximation. The role of the interaction potential and of the applied electric field, which mix the energy states according to different quantum numbers and create sy…
We demonstrate the absence of a DC Stark shift in an ytterbium optical lattice clock. Stray electric fields are suppressed through the introduction of an in-vacuum Faraday shield. Still, the effectiveness of the shielding must be experimentally assessed. Such diagnostics are accomplished by applying high voltage to six electrodes, which are grounded in normal operation to form part of the Faraday shield. Our measurements place a constraint on the DC Stark shift at the $10^{-20}$ level, in units of the clock frequency. Moreover, we discuss a potential source of error in strategies to precisely …
A strong, far-detuned laser can shift the energy levels of an optically active quantum system via the AC Stark effect. We demonstrate that the polarization of the laser results in a spin-selective modification to the energy structure of a charged quantum dot, shifting one spin manifold but not the other. An additional shift occurs due to the Overhauser field of the nuclear spins, which are pumped into a partially polarized state. This mechanism offers a potentially rapid, reversible, and coherent control of the energy structure and polarization selection rules of a charged quantum dot.
A new perspective on how to manipulate molecules by means of very strong laser pulses is emerging with insights from the so-called light-induced potentials, which are the adiabatic potential energy surfaces of molecules severely distorted by the effect of the strong field. Different effects appear depending on how the laser frequency is tuned, to a certain electronic transition, creating light-induced avoided crossings, or very off-resonant, generating Stark shifts. In the former case it is possible to induce dramatic changes in the geometry and redistribution of charges in the molecule while …
Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping
Tsinghua University（清华大学）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）
This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the non-relativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is lnear in the…
We bring the set of linear quantum operations, important for many fundamental studies in photonic systems, to the material domain of collective excitations known as spin waves. Using the ac Stark effect we realize quantum operations on single excitations and demonstrate a spin-wave analogue of Hong-Ou-Mandel effect, realized via a beamsplitter implemented in the spin wave domain. Our scheme equips atomic-ensemble-based quantum repeaters with quantum information processing capability and can be readily brought to other physical systems, such as doped crystals or room-temperature atomic ensemble…
Theory of vibrational Stark effect for adsorbates and diatomic molecules
CAS Key Laboratory of Quantum Information, University of Science and Technology of China（中国科学院量子信息重点实验室，中国科学技术大学）；Hefei National Research Center for Physical Sciences at Microscale（合肥微尺度物质科学国家研究中心）；Department of Chemistry, University of Science and Technology of China（中国科学技术大学化学系）；Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学量子信息与量子物理协同创新中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
We report on a method for measuring ac Stark shifts observed in stored light experiments while simultaneously determining the energetic splitting between the electronic ground states involved in the two-photon transition. To this end we make use of the frequency matching effect in light storage spectroscopy. We find a linear dependence on the intensity of the control field applied during the retrieval phase of the experiment. At the same time, we observe that the light shift is insensitive to the intensity of the signal field which is in contrast to continuously operated schemes using electrom…
The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic $XY$ spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the …
Stark effect of hydrogenic ions as a test of the indefinite-metric formalism of the eight-component relativistic wave equation for spin-$\frac{1}{2}$ particles
Center for Theoretical Physics, Faculty of Science, Parahyangan Catholic University（帕拉希扬天主教大学理学院理论物理中心）
该论文通过计算氢离子 Stark 位移验证了八分量相对论波动方程的不定度规形式体系，证明其与 Dirac 结果一致，并揭示了自旋-场耦合和负范数态的必要性。
Atomistic tight-binding (TB) simulations are performed to calculate the Stark shift of the hyperfine coupling for a single Arsenic (As) donor in Silicon (Si). The role of the central-cell correction is studied by implementing both the static and the non-static dielectric screenings of the donor potential, and by including the effect of the lattice strain close to the donor site. The dielectric screening of the donor potential tunes the value of the quadratic Stark shift parameter ($η_2$) from -1.3 $\times$ 10$^{-3} μ$m$^2$/V$^2$ for the static dielectric screening to -1.72 $\times$ 10$^{-3} μ$…
We propose a combination of Electromagnetically Induced Transparency (EIT)/Raman and pulsed spectroscopy techniques to accurately cancel frequency shifts arising from EIT fields in forbidden optical lattice clock transitions of alkaline earth atoms. Time-separated laser pulses are designed to trap atoms in coherent superpositions while eliminating off-resonance ac Stark contributions at particular laser detunings from the intermediate excited state. The scheme achieves efficient population transfer up to 60% with potential inaccuracy $<$ $10^{-17}$. Cancellation of external light shifts determ…
A simple 1-D relativistic model for a diatomic molecule with a double point interaction potential is solved exactly in a constant electric field. The Weyl-Titchmarsh-Kodaira method is used to evaluate the spectral density function, allowing the correct normalization of continuum states. The boundary conditions at the potential wells are evaluated using Colombeau's generalized function theory along with charge conjugation invariance and general properties of self-adjoint extensions for point-like interactions. The resulting spectral density function exhibits resonances for quasibound states whi…
We evaluate the polarizabilities of the 5p_{1/2}, 6s, 6p_{1/2}, and 6p_{3/2} states of In using two different high-precision relativistic methods: linearized coupled-cluster approach where single, double and partial triple excitations of the Dirac-Fock wave function are included to all orders of perturbation theory and an approach that combines the configuration interaction and the coupled-cluster method. Extensive comparison of the accuracy of these methods is carried out. The uncertainties of all recommended values are evaluated. Our result for the 6s-5p_{1/2} Stark shift is in excellent agr…
Demonstrating the quantum-confined Stark effect (QCSE) in silicon nanocrystals (NCs) embedded in oxide has been rather elusive, unlike the other materials. Here, the recent experimental data from ion-implanted Si NCs is unambiguously explained within the context of QCSE using an atomistic pseudopotential theory. This further reveals that the majority of the Stark shift comes from the valence states which undergo a level crossing that leads to a nonmonotonic radiative recombination behavior with respect to the applied field. The polarizability of embedded Si NCs including the excitonic effects …
We conducted series of experiments on observing a Stark-type effect in superfluid $^4$He in presence of relative laminar flows of the normal and superfluid components. It is designed a measurement cell which allows us to simultaneously create hydrodynamic flows in the liquid and to carry out high-frequency radio-measurements at external electric field. We used a dielectric disk resonator that made possible to cover a wide frequency range. In our experiments it was registered the spectrum of the dielectric disk resonator modes, as well as narrow lines of absorption of a microwave radiation in H…
