Linear Stark Research Articles

The electric dipole moment of the electron: An intuitive explanation for the evasion of Schiff’s theorem

In most experimental searches for the electron electric dipole moment, one searches for a linear Stark effect in a paramagnetic atom or molecule and interprets the result in terms of the electric dipole moment of the unpaired valence electron(s). Schiff’s theorem states that in the limit of nonrelativistic quantum mechanics, there can be no linear Stark effect to first order in the electric dipole moment. Sandars has shown that Schiff’s theorem is not applicable when special relativity is taken into account. We give a heuristic explanation for this relativistic effect, which corrects a widespread misconception in the literature.

Dipole transitions and Stark effect in the charge-dyon system

We consider the dipole transitions and the linear and quadratic Stark effects in the MICZ-Kepler system interpreted as a charge-dyon system. We show that while the linear Stark effect in the ground state is proportional to the azimuth quantum number (and to the sign of the monopole number), the quadratic Stark effect in the ground state is independent of the signs of the azimuth and monopole numbers.

Erratum: Linear Stark Shift in Dressed Atoms as a Signal to Measure a Nuclear Anapole Moment with a Cold-Atom Fountain or Interferometer [Phys. Rev. Lett.98, 043003 (2007)

Erratum: Linear Stark Shift in Dressed Atoms as a Signal to Measure a Nuclear Anapole Moment with a Cold-Atom Fountain or Interferometer [Phys. Rev. Lett.<b>98</b>, 043003 (2007)

Observation of the Linear Stark Effect in a Single Acceptor in Si

The Stark splitting of a single fourfold degenerate impurity located within the built-in potential of a metal-semiconductor contact is investigated using low temperature transport measurements. A model is developed and used to analyze transport as a function of temperature, bias voltage, and magnetic field. Our data is consistent with a boron impurity. We report g factors of g_{1/2}=1.14 and g_{3/2}=1.72 and a linear Stark splitting 2Delta of 0.1 meV.

Linear Stark Shift in Dressed Atoms as a Signal to Measure a Nuclear Anapole Moment with a Cold-Atom Fountain or Interferometer

We demonstrate theoretically the existence of a linear dc Stark shift of the individual substates of an alkali atom in its ground state, dressed by a circularly polarized laser field. It arises from the electroweak nuclear anapole moment violating P but not T. It is characterized by the pseudoscalar xi k wedge E x B involving the photon angular momentum and static electric and magnetic fields. We derive the relevant left-right asymmetry with its complete signature in a field configuration selected for a precision measurement with cold-atom beams. The 3, 3 --> 4, 3 Cs transition frequency shift amounts to 7 microHz for a laser power of approximately 1 kW at 877 nm, E=100 kV/cm and B approximately > 0.5 G.

A linear Stark shift in dressed atoms as a signal to measure a nuclear anapole moment with a cold atom fountain or interferometer

A linear Stark shift in dressed atoms as a signal to measure a nuclear anapole moment with a cold atom fountain or interferometer

Optical Stark spectroscopy of solids

Optical Stark spectroscopy of solids has been closely associated with Alexander Kaplyanskii over the last four decades. The field is reviewed here with some emphasis on the use of spectral hole burning and coherent transient techniques to measure linear and quadratic Stark coefficients. Examples are drawn from a wide range of materials including transition metal and rare-earth-doped insulators, color centers, organic molecular solids and semiconductors. Tabulation of data drawn from the literature of the last 50 years is juxtaposed to give some perspective and suggest material, which might benefit from future application of high-resolution spectroscopic techniques.

Spontaneous switching of permanent dipoles in single conjugated polymer molecules

Electric fields applied in low temperature single molecule spectroscopy of conjugated polymers open a direct window to the microscopic charge distribution within the individual molecule. We typically observe a linear Stark effect, characteristic of either an internal electric field within the molecule or a difference in polarisation of ground and excited state. Here, we report evidence for spontaneous switching of the permanent dipole responsible for the shift in emission with field in a ladder-type polymer. This switching most likely results from photoinduced radical formation and annihilation and can be linked to blinking in single molecules and nanocrystal quantum dots.

Water vapor at a translational temperature of1K

We report the creation of a confined slow beam of heavy-water $({\mathrm{D}}_{2}\mathrm{O})$ molecules with a translational temperature around $1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. This is achieved by filtering slow ${\mathrm{D}}_{2}\mathrm{O}$ from a thermal ensemble with inhomogeneous static electric fields exploiting the quadratic Stark shift of ${\mathrm{D}}_{2}\mathrm{O}$. All previous demonstrations of electric-field manipulation of cold dipolar molecules rely on a predominantly linear Stark shift. Further, on the basis of elementary molecular properties and our filtering technique we argue that our ${\mathrm{D}}_{2}\mathrm{O}$ beam contains molecules in only a few rovibrational states.

Controlled Stark shifts in Er3+-doped crystalline and amorphous waveguides for quantum state storage

We present measurements of the linear Stark effect on the 4I15/2→4I13/2 transition in an Er3+-doped proton-exchanged LiNbO3 crystalline waveguide and an Er3+-doped silicate fiber. The measurements were made using spectral hole burning techniques at temperatures below 4K. We measured an effective Stark coefficient (Δμeχ)/(h)=25±1kHz/Vcm−1 in the crystalline waveguide and (Δμe¯χ)/(h)=15±1kHz/Vcm−1 in the silicate fiber. These results confirm the potential of erbium-doped waveguides for quantum state storage based on controlled reversible inhomogeneous broadening.

Photon Echoes Produced by Switching Electric Fields

We demonstrate photon echoes in Eu3+:Y2SiO5 by controlling the inhomogeneous broadening of the Eu3+ 7F0<-->5D0 optical transition. This transition has a linear Stark shift, and we induce inhomogeneous broadening by applying an external electric field gradient. After optical excitation, reversing the polarity of the field rephases the ensemble, resulting in a photon echo. This is the first demonstration of such a photon echo, and its application as a quantum memory is discussed.

How single conjugated polymer molecules respond to electric fields

Conjugated polymers find applications in a range of devices such as light-emitting diodes, field-effect transistors and solar cells. The elementary electronic response of these semiconductors to electric fields is understood in terms of nanoscale perturbations of charge density. We demonstrate a general breaking of spatial charge symmetry by considering the linear Stark effect in the emission of single chromophores on individual chains. Spectral shifts of several nanometres occur due to effective dipoles exceeding 10 D. Although the electric field does not ionize the exciton, some molecules exhibit field-induced intensity modulations. This quenching illustrates the equivalence of charge symmetry breaking and polaron-pair or charge-transfer-state formation, and provides a microscopic picture of permanent charging, which leads to doping and exciton dissociation in actual devices. In addition to using this tuneable emission in single-photon electro-optic modulators, hysteresis in the Stark shift suggests a route to designing nanoscale memory elements such as molecular switches.

Linear Stark effect of CdS/HgS/CdS spherical nanometric system

Electronic energy and wave function of three-layer spherical nanometric system in homogeneous electric field is solved, the influence of applied field and sample size to the shift of Stark energy level is discussed.

Membrane potential detection with second-harmonic generation and two-photon excited fluorescence: A theoretical comparison

We theoretically compare the performance of TPEF and SHG microscopy for membrane potential imaging. We argue that electrochromic TPEF and SHG membrane potential responses are reflections of the same phenomenon, and can be described in a unified manner as resulting from the linear Stark effect. We also show that TPEF and SHG exhibit similar sensitivities in the case of both electrochromic and orientational response mechanisms. Despite their similar sensitivities, SHG nevertheless presents advantages over TPEF for membrane potential imaging because of its remarkable spatial and spectral contrast, and because of its insensitivity to non-radiative excited-state damping mechanisms.

Heavy Rydberg states

This paper discusses the nature of heavy Rydberg states, i.e. quantum states in molecular systems that are bound by the almost pure Coulomb potential between pairs of ions. A theoretical framework is developed in terms of mass–scaling laws for heavy Rydberg systems of certain reduced mass, so that the physics of electronic Rydberg states can be straightforwardly applied to heavier ion–pair systems, or any other system bound by a 1/r potential. The general description of such quantum systems is supported by an experimental investigation of the energy region near the H+H− ion–pair dissociation limit, using a 1 XUV + 1 UV laser excitation scheme. Such a scheme allows for preparation of a single intermediate rovibrational quantum state, from which the ion–pair threshold region can be explored with a narrowband Fourier–transform limited laser. Field–induced lowering of the H+H− dissociation limit was observed in the presence of an electric field. Using a combination of DC and pulsed electric fields two–photon induced threshold ion–pair production spectroscopy (TIPPS) was performed for a variety of field strengths. Below the field–dissociation limit coherent wave packets of bound heavy Rydberg states are excited in an electric field. The coherent evolution of the Stark states, giving rise to oscillations in angular momentum space, can be quantitatively understood in terms of the linear Stark effect in the hydrogen atom, where the light electron is replaced by the heavier H− particle. The dynamics of wave packets of heavy Rydberg states is slower than in ordinary electronic Rydberg states, according to their larger mass. For a wide variety of binding energy and external electric field, the observed oscillation frequencies of the Stark wave packets match this model. An important parameter describing the specific properties of the H+H− Rydberg states is the scaled lifetime, which may be considered as a material constant, and it is determined atτ= (5.8±2.0)×10−21 s n 4.

Quantum electrical dipole in triangular systems: A model for spontaneous polarity in metal clusters

Triangular symmetric molecules with mirror symmetry perpendicular to the 3-fold axis are forbidden to have a fixed electrical dipole moment. However, if the ground state is orbitally degenerate and lacks inversion symmetry, then a ``quantum'' dipole moment does exist. The system of 3 electrons in D_3h symmetry is our example. This system is realized in triatomic molecules like Na_3. Unlike the fixed dipole of a molecule like water, the quantum moment does not point in a fixed direction, but lies in the plane of the molecule and takes quantized values +/- mu_0 along any direction of measurement in the plane. An electric field F in the plane leads to a linear Stark splitting +/- mu_0 F}. We introduce a toy model to study the effect of Jahn-Teller distortions on the quantum dipole moment. We find that the quantum dipole property survives when the dynamic Jahn-Teller effect is included, if the distortion of the molecule is small. Linear Stark splittings are suppressed in low fields by molecular rotation, just as the linear Stark shift of water is suppressed, but will be revealed in moderately large applied fields and low temperatures. Coulomb correlations also give a partial suppression.

NONCOMMUTATIVE CORRECTIONS TO THE MIC–KEPLER HAMILTONIAN

Noncommutative corrections to the MIC–Kepler system (i.e. hydrogen atom in the presence of a magnetic monopole) are computed in Cartesian and spherical coordinates. In the framework of perturbation theory we were able to derive noncommutative corrections to the MIC–Kepler spectrum. We also found a nontrivial contribution to the linear Stark effect which did not exist in the standard hydrogen model.

Adiabatic Bohr-Sommerfeld calculations for the hydrogenic Stark effect

A general prescription is presented for the semiclassical calculation of quantized energy levels of a class of parametric quantum systems. Starting with the Bohr-Sommerfeld quantization conditions of an exactly solvable system in parabolic coordinates, the calculation evolves the classical equations of motion while adiabatically introducing a nonzero parameter. We present accurate results for the quadratic Stark effect in addition to the linear Stark effect, an improvement over previous semiclassical studies.

A quasi-analytic model of a linear Stark accelerator/decelerator for polar molecules

This article describes a quasi-analytic model of a linear Stark accelerator/decelerator for polar molecules in both their low- and high-field seeking states, and examines the dynamics of the acceleration/deceleration process and its phase stability. The requisite time-dependent inhomogeneous Stark fields, used in current experiments, are Fourier-analyzed and found to consist of a superposition of partial waves with well-defined phase velocities. The kinematics of the interaction of molecules with the partial waves is discussed and the notion of a phase of a molecule in a travelling field is introduced. Next, the net potential and the net force that act on the molecules are derived. A special case, the first-harmonic accelerator/decelerator, is introduced. This represents a model system many of whose properties can be obtained analytically. The first-harmonic accelerator/decelerator dynamics is presented and discussed along with that of the isomorphic biased-pendulum problem. Finally, the general properties of the velocity of the molecules in a phase-stable accelerator/decelerator are examined.

Development of the motional Stark effect with laser-induced fluorescence diagnostic

The motional Stark effect diagnostic (MSE) is presently a widely accepted technique for measuring the magnetic field pitch angle in high field (&amp;gt;1 T) plasma devices. A hydrogen neutral beam passing through a magnetic field perceives υ×B electric field, and its Balmer-α spectral emission is split and polarized by the linear Stark effect. The technique cannot be readily used at lower magnetic fields, due to loss of polarization fraction when lines of different polarization overlap due to line broadening which is on the order of the separation. This article describes the development of a technique to extend the capability of MSE to include lower fields (0.01 T and up) and the field magnitude as well as direction. The technique employs laser-induced fluorescence on a diagnostic neutral beam. The narrow-band laser and low energy spread neutral beam allow the observed linewidths to be significantly narrower than these observed from previously employed collisionally induced fluorescence systems.