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arXiv:2608.19712 · Physical Review A

Internal cyclotron probe of the vertical polarizability of a surface-state electron on helium

Anonymous

Published Jul 22, 2026• 0 citations
arXivHTMLPDF

Abstract

We study a surface-state electron on liquid helium in a tilted magnetic field. The tilt couples the cyclotron ladder to the vertical Rydberg-like subbands of the same electron and thereby realizes a self-coupled Landau-subband Hamiltonian. In the far-detuned regime, the cyclotron line acquires a state-dependent shift described by standard second-order perturbation theory. The resulting expression identifies the cyclotron resonance as a direct probe of the dynamical polarizability of the vertical ladder. The theory is intrinsically multilevel. Exact diagonalization confirms a broad microwave window in which sizable state-dependent cyclotron shifts are expected while the system remains dispersive.

DOI
10.1103/96p7-vj9f

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We study a surface-state electron on liquid helium in a tilted magnetic field. The tilt couples the cyclotron ladder to the vertical Rydberg-like subbands of the same electron and thereby realizes a self-coupled Landau-subband Hamiltonian. In the far-detuned regime, the cyclotron line acquires a state-dependent shift described by standard second-order perturbation theory. The resulting expression identifies the cyclotron resonance as a direct probe of the dynamical polarizability of the vertical ladder. The theory is intrinsically multilevel. Exact diagonalization confirms a broad microwave window in which sizable state-dependent cyclotron shifts are expected while the system remains dispersive.
Radio-frequency reflectometry, which probes small changes in the electrical impedance of a device, provides a useful method for sensitive and fast detection of dynamic processes in quantum systems. We use this method to detect excitation of the quantized motional (Rydberg) states of trapped electrons on liquid helium. The Rydberg transition in an ensemble of electrons is detected by a change in the impedance of an rf circuit coupled to the microwave-excited electrons. To elucidate the origin of the observed response, the result is compared with an independent impedance measurement on the same electron system modulated by an electrostatic potential and with a numerical simulation using the Green's function method. Additionally, it is found that the rf response to the Rydberg resonance can be strongly enhanced by a resonant mode of the electron collective motion. Our results suggest that the observed response to the Rydberg resonance must be attributed to the lateral motion of the many-electron system rather than the vertical displacement of the individually excited electrons, as was explicate earlier. A theoretical analysis of the expected response due to the vertical displacement is given.
A single electron in a quantum cyclotron yields new measurements of the electron magnetic moment, given by g/2 = 1.00115965218073(28)[0.28 ppt], and the fine structure constant, α −1 = 137.035999084(51)[0.37 ppb], both significantly improved from prior results. The static magnetic and electric fields of a Penning trap confine the electron, and a 100 mK dilution refrigerator cools its cyclotron motion to the quantum-mechanical ground state. A quantum nondemolition measurement allows resolution of single cyclotron jumps and spin flips by coupling the cyclotron and spin energies to the frequency of the axial motion, which is self-excited and detected with a cryogenic amplifier. The trap electrodes form a high-Q microwave resonator near the cyclotron frequency; coupling between the cyclotron motion and cavity modes can inhibit spontaneous emission by over 100 timesthe free-space rate and shiftthe cyclotron frequency, a systematic effect that dominated the uncertainties of previous g-value measurements. A cylindrical trap geometry creates cavity modes with analytically calculable couplingsto cyclotron motion. Two independent methods use the cyclotron damping rate of an electron plasma or of the single electron itself as probes of the cavity mode structure and allow the identification ofthe modes by their geometries and couplings, the quantification of an offset between the mode and electrostatic centers, and the reduction of the cavity shift uncertainty to sub-dominant levels. Measuring g at four magnetic fields with cavity shifts spanning thirty times the final g-value uncertainty provides a check on the calculated cavity shifts. Magnetic field fluctuations limit the measurement of g by adding a noise-model dependence to the extraction of the cyclotron and anomaly frequencies from their resonance lines; the relative agreement of two line-splitting methods quantifies a lineshape model uncertainty. New techniques promise to increase field stability, narrow the resonance lines, and accelerate the measurement cycle. The measured g allows tests for physics beyond the Standard Model through searches for its temporal variation and comparisons with a “theoretical” g-value calculated from quantum electrodynamics and an independently measured fine structure constant.
In a two-dimensional electron gas, a strong perpendicular magnetic field confines electrons to quantized cyclotron orbits, giving rise to Landau levels with discrete orbit radii. Even the smallest Landau orbit, set by the magnetic length, spans tens of nanometers for fields of a few Tesla, imposing an intrinsic nonlocal response to electromagnetic excitations. From a microscopic theory of the nonlocal susceptibility, we derive the Green's function, the central quantity governing all electromagnetic interactions, and evaluate Purcell factors, Lamb shifts, and emission spectra from a proximal dipole emitter beyond the Markov and rotating-wave approximations. Significant nonlocal effects resulting from spatial dispersion of the Landau level response modify the response for experimentally relevant situations up to distances of hundreds of nanometers and, in particular, brighten locally dipole-forbidden transitions due to near-field gradients at multiples of the cyclotron frequency. The relevant length scales are typical of state-of-the-art nanostructured terahertz architectures, and some of our nonlocal features are consistent with recent experiments using Landau level polaritons.
Ponderomotive energy shifts experienced by Rydberg atoms in optical fields are known to be well approximated by the classical quiver energy of a free electron. We examine such energy shifts quantum mechanically and elucidate how they relate to the ponderomotive shift of a free electron in off-resonant fields. We derive and evaluate corrections to the ponderomotive free-electron polarizability in the length and velocity (transverse or Coulomb) gauges, which agree exactly as mandated by the gauge invariance. We also show how the free electron value emerges from the Dirac equation through summation over the Dirac sea states. We find that the free-electron ac Stark shift comes as an expectation value of a term proportional to the square of the vector potential in the velocity gauge. On the other hand, the same dominant contribution can be obtained to first order via a series expansion of the exact energy shift from the second-order perturbation theory in the length gauge. Finally, we numerically examine the validity of the free-electron approximation. The correction to the free-electron value becomes smaller with increasing principal quantum number, and it is well below a percent for 60sss states of Rb and Sr away from the resonances.
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 13\frac{1}{3}31​ and 12\frac{1}{2}21​ filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to the effect of band-mass anisotropy.
We present measurements of the resonant microwave excitation of Rydberg energy levels for surface-state electrons on superfluid helium. The temperature-dependent contribution to the linewidth gamma(T) agrees with theoretical predictions and is very small below 700 mK, in the ripplon scattering regime. Absorption saturation and power broadening were observed as the fraction of electrons in the first excited state was increased to 0.49, close to the thermal excitation limit of 0.5. The Rabi frequency Omega was determined as a function of microwave power. High values of the ratio Omega/gamma confirm this system as an excellent candidate for creating qubits.