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 applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter.
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
For atoms described by a 1-dimensional Friedrichs model we present the following result: pre-existing resonances, when subjected to a small constant electric field (DC Stark effect), are unstable in the weak field limit. In contrast, pre-existing resonances under the influence of a small time-periodic electric field (AC Stark effect) are stable in this limit. This article is a review of our results in "Instability of pre-existing resonances under a small constant electric field", arXiv:1310.4745.
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.
We will study the splitting in the energy spectrum of the hydrogen atom subjected to a uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases not degenerate ($n=1$) and degenerate ($n=2$), along with known results of corrections in these levels caused by the minimum length applied purely to the hydrogen atom, so that we may find and estimate the corrections of minimum length applied to the Stark effect.
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the low-lying eigenvalues. This shows that the excitation frequencies are proportional to the square root of the boundary curvature at a certain point determined by the direction of the electric field.
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…
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 obtained accurate resonances for the Stark effect in hydrogen by means of three independent methods. Two of them are based on complex rotation of the coordinates and diagonalization of the Hamiltonian matrix (CRLM and CRCH). The other one is based on the Riccati equations for the logarithmic derivatives of factors of the wavefunction (RPM). The latter approach enabled us to obtain the most accurate results and extremely sharp resonances.
By invoking supersymmetry, we found a condition under which the Stark effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable. The exact solvability condition for the interaction parameters involved yields exact wavefunction for the "stretched" states, $|J=m,m>$, and for the $|1,1>$ state in the case of a purely induced-dipole interaction. The analytic expressions for the eigenenergy, the space-fixed dipole moment, the alignment cosine, and the expectation value of the angular momentum allow to readily reverse-engineer the problem of …
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…
We study the quantum-confined Stark effect in single InAs/GaAs quantum dots embedded within a AlGaAs/GaAs/AlGaAs quantum well. By significantly increasing the barrier height we can observe emission from a dot at electric fields of -500 kV/cm, leading to Stark shifts of up to 25 meV. Our results suggest this technique may enable future applications that require self-assembled dots with transitions at the same energy.
Studies of atomic systems in electric fields are challenging because of the diverging perturbation series. However, physically meaningful Stark shifts and ionization rates can be found by analytical continuation of the series using appropriate branch cut functions. We apply this approach to low-dimensional hydrogen atoms in order to study the effects of reduced dimensionality. We find that modifications by the electric field are strongly suppressed in reduced dimensions. This finding is explained from a Landau-type analysis of the ionization process.
Inhomogeneous broadening is a major limitation for the application of quantum emitters in hBN to integrated quantum photonics. Here we demonstrate that blue emitters with an emission wavelength of 436 nm are less sensitive to electric fields than other quantum emitter species in hBN. Our measurements of Stark shifts indicate negligible transition dipole moments for these centers with dominant quadratic stark effect. Using these results, we employed DFT calculations to identify possible point defects with small transition dipole moments, which may be the source of blue emitters in hBN.
We study the entanglement properties of two three-level Rydberg atoms passing through a single-mode cavity. The interaction of an atom with the cavity field allows the atom to make a transition from the upper most (lower most) to the lower most (upper most) level by emission (absoprtion) of two photons via the middle level. We employ an effective Hamiltonian that describes the system with a Stark shifted two-photon atomic transition. We compute the entanglement of formation of the joint two-atom state as a function of Rabi angle $gt$. It is shown that the Stark shift can be used to enhance the…
We propose a method to read-out the spin-state of an electron in a quantum dot in a Voigt geometry magnetic field using cycling transitions induced by the AC Stark effect. We show that cycling transitions can be made possible by a red-detuned, circularly-polarized laser, which modifies the spin eigenstates and polarization selection rules via the AC Stark effect. A Floquet-Liouville supermatrix approach is used to calculate the time-evolution of the density matrix under the experimental conditions of a spin read-out operation. With an overall detection efficiency of 2.5%, the read-out is a sin…
The extrinsic dephasing of a hole spin confined to a self-assembled quantum dot is dominated by charge noise acting on an electric-field dependent g-factor. Here we propose the use of the optical Stark effect to reduce the sensitivity of the effective hole Zeeman energy to fluctuations in the local electric-field. Calculations using measured quantum dot parameters are presented, and demonstrate a factor of 10-100 reduction in the extrinsic dephasing. Compared to active stabilization methods, this technique should benefit from reduced experimental complexity.
Single photon emitters (SPEs) are critical building blocks needed for quantum science and technology. For practical applications, large-scale room-temperature solid-state platforms are required. Color centers in layered hexagonal boron nitride (hBN) have recently been found to be ultra-bright and stable SPEs at room temperature. Yet, to scale up solid-state quantum information processing, large tuning range of single photon energy is demanded for wavelength division multiplexing quantum key distribution, where indistinguishability is not required, and for indistinguishable single-photon produc…
The effect of an external applied electric field on the electronic ground state energy of a quantum box with a geometry defined by a wedge is studied by carrying out a variational calculation. This geometry could be used as an approximation for a tip of a cantilever of an atomic force microscope. We study theoretically the Stark effect as function of the parameters of the wedge: its diameter, angular aperture and thickness; as well as function of the intensity of the external electric field applied along the axis of the wedge in both directions; pushing the carrier towards the wider or the nar…
A superconducting qubit was driven in an ultrastrong fashion by an oscillatory microwave field, which was created by coupling via the nonlinear Josephson energy. The observed Stark shifts of the `atomic' levels are so pronounced that corrections even beyond the lowest-order Bloch-Siegert shift are needed to properly explain the measurements. The quasienergies of the dressed two-level system were probed by resonant absorption via a cavity, and the results are in agreement with a calculation based on the Floquet approach.
We propose a spin manipulation technique based entirely on electric fields applied to acceptor states in $p$-type semiconductors with spin-orbit coupling. While interesting in its own right, the technique can also be used to implement fault-resilient holonomic quantum computing. We explicitly compute adiabatic transformation matrix (holonomy) of the degenerate states and comment on the feasibility of the scheme as an experimental technique.
We investigate the error due to D.C. Stark effect for quantum information processing for trapped ion quantum computers using the scalable architecture proposed in J. Res. Natl. Inst. Stan. 103, 259 (1998) and Nature 417, 709 (2002). As the operation speed increases, dephasing and decoherence due to the D.C. Stark effect becomes prominent as a large electric field is applied for transporting ions rapidly. We estimate the relative significance of the decoherence and dephasing effects and find that the latter is dominant. We find that the minimum possible of dephasing is quadratic in the time of …
We present Floquet-Keldysh non-equilibrium dynamical mean field calculations (DMFT) with an iterative perturbative solver (IPT) for high pump-power induced Stark states yielding a closing gap within semiconductor bulk and nano-cavities. Our model predicts unusual broadening of bands in systems like ZnO random lasers. This can be explained as an exciton-polariton coupling within the single crystalline pillar meeting the Mie resonance condition. Extraordinary enhancement of the lifetime of electronic states within the gap can lead to stable lasing modes and gain narrowing.
We show that the resonances of the Stark effect in hydrogen reported in Phys. Rev. A \textbf{88}, 022509 (2013) are considerably less accurate than the number of digits appear to suggest. In particular, the imaginary part of the lowest resonance is several orders of magnitude greater than it should be. We compare the results of that paper with those provided by the Riccati-Padé method, perturbation theory and an asymptotic expansion for the resonance width. The inaccuracy of those results can be traced back to the lack of precision in the calculation of the matrix elements of the secular equat…
This article describes the AC Stark, Stern-Gerlach, and Quantum Zeno effects as they are manifested during continuous interferometric measurement of a two-state quantum system (qubit). A simple yet realistic model of the interferometric measurement process is presented, and solved to all orders of perturbation theory in the absence of thermal noise. The statistical properties of the interferometric Stern-Gerlach effect are described in terms of a Fokker-Plank equation, and a closed-form expression for the Green's function of this equation is obtained. Thermal noise is added in the form of a ex…
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 that two initially non-resonant quantum dots may be brought into resonance by the application of a single detuned laser. This allows for control of the inter-dot interactions and the generation of highly entangled excitonic states on the picosecond timescale. Along with arbitrary single qubit manipulations, this system would be sufficient for the demonstration of a prototype excitonic quantum computer.
The scattering theory of Lax and Phillips, originally developed to describe resonances associated with classical wave equations, has been recently extended to apply as well to the case of the Schroedinger equation in the case that the wave operators for the corresponding Lax-Phillips theory exist. It is known that the bound state levels of an atom become resonances (spectral enhancements) in the continuum in the presence of an electric field (in all space) in the quantum mechanical Hilbert space. Such resonances appear as states in the extended Lax-Phillips Hilbert space. We show that for a si…
The broadening of lines by Stark effect is an important tool for inferring electron density and temperature in plasmas. Stark-effect calculations often rely on atomic data (transition rates, energy levels,...) not always exhaustive and/or valid for isolated atoms. We present a recent development in the detailed opacity code SCO-RCG for K-shell spectroscopy (hydrogen- and helium-like ions). This approach is adapted from the work of Gilles and Peyrusse. Neglecting non-diagonal terms in dipolar and collision operators, the line profile is expressed as a sum of Voigt functions associated to the St…
The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves a generalized hypergeometric function ${}_{3}F_{2}$ with the unit argument. Numerical values of the polarizabilities for relativistic planar hydrogenic atoms with atomic numbers $1\leqslant Z\leqslant68$ are provided …
We propose a frequency-mixed effect of Terahertz (THz) and Gigahertz (GHz) electromagnetic waves in the cryogenic system of electrons floating on liquid helium surface. The THz wave is near-resonant with the transition frequency between the lowest two levels of surface state electrons. The GHz wave does not excite the transitions but generates a GHz-varying Stark effect with the symmetry-breaking eigenstates of electrons on liquid helium. We show an effective coupling between the inputting THz and GHz waves, which appears at the critical point that the detuning between electrons and THz wave i…
We study effects of weak nonlineary on localization of waves in disordered Stark ladder corresponding to propagation in presence of disorder and a static field. Our numerical results show that nonlinearity leads to delocalization with subdiffusive spreading along the ladder. The exponent of spreading remains close to its value in absence of the static field.
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 …
The effective Hamiltonian describing resonant interaction of an ensemble of identical quantum particles with a photon-free vacuum electromagnetic field has been obtained with allowance for the second-order terms over the coupling constant (the Stark interaction) by means of the perturbation theory on the basis of the unitary transformation of the system quantum state. It has been shown that in the Markov approximation the effective Hamiltonian terms of the first-order coupling constant are represented as the quantum Wiener process, whereas the second-order terms are expressed by the quantum Po…
In the present work, the effect of AC-Stark shift (i.e. light-shift) in optical dipole trap on in-situ absorption probe imaging of the trapped atoms has been investigated. We have calculated the light-shift of various energy levels of $^{87}$Rb atoms relevant for trapping in an optical dipole trap (ODT). The spatial varying intensity of the ODT beam results in position dependent light-shift (i.e. AC-Stark shift). Such modifications in the energy levels of the atom result in modification in the absorption cross-section, which finally modifies the optical density (OD) in in-situ absorption imagi…
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…
We investigate and compare experimental and numerical excitonic spectra of the yellow series in cuprous oxide Cu$_2$O in the Voigt configuration and thus partially extend the results from Schweiner et al. [Phys. Rev. B 95, 035202 (2017)], who only considered the Faraday configuration. The main difference between the configurations is given by an additional effective electric field in the Voigt configuration, caused by the motion of the exciton through the magnetic field. This Magneto-Stark effect was already postulated by Gross et al. and Thomas et al. in 1961 [Sov. Phys. Solid State 3, 221 (1…
We develop a time-dependent Schrieffer-Wolff-Lindblad perturbation theory to study effective interactions for driven open quantum systems. The starting point of our analysis is a given Lindblad equation, based on which we obtain an effective (averaged) map that describes the renormalization of both the Hamiltonian and collapse operators due to the drive. As a case study, we apply this method to the dispersive readout of a transmon qubit and derive an effective disperive map that describes measurement-induced dephasing and Stark shift for the transmon. The effective map we derive is completely …
Using a semi-classical approach, we derive a fully analytical expression for the ionization rate of excitons in two-dimensional materials due to an external static electric field, which eliminates the need for complicated numerical calculations. Our formula shows quantitative agreement with more sophisticated numerical methods based on the exterior complex scaling approach, which solves a non-hermitian eigenvalue problem yielding complex energy eigenvalues, where the imaginary part describes the ionization rate. Results for excitons in hexagonal boron nitride and the $A-$exciton in transition …
