We present measurements of the resonant microwave absorption between the Rydberg energy levels of surface-state electrons on the surface of superfluid liquid helium, in the frequency range 165-220 GHz. The resonant frequency was temperature dependent. The experiments are in agreement with recent theoretical calculations of the renormalization of the electron energy levels due to zero-point and thermal ripplons. The temperature-dependent contribution to the line width gamma(T) for excitation to the first excited state at 189.6 GHz is compared with other measurements and theoretical predictions.

We study the shift of the energy levels of electrons on a helium surface due to the coupling to the quantum field of surface vibrations. As in quantum electrodynamics, the coupling is known, and it is known to lead to an ultraviolet divergence of the level shifts. We show that there are diverging terms of different nature and use the Bethe-type approach to show that they cancel each other, to leading order. This resolves the long-standing theoretical controversy and explains the existing experiments. The results allow us to study the temperature dependence of the level shift. The predictions are in good agreement with the experimental data, with no adjustable parameters.

We study nonlinear inter-subband microwave absorption of electrons bound to the liquid helium surface. Already for a comparatively low radiation intensity, resonant absorption due to transitions between the two lowest subbands is accompanied by electron overheating. The overheating results in a significant population of higher subbands. The Coulomb interaction between electrons causes a shift of the resonant frequency, which depends on the population of the excited states and thus on the electron temperature $T_e$. The latter is determined experimentally from the electron photoconductivity. The experimentally established relationship between the frequency shift and $T_e$ is in reasonable agreement with the theory. The dependence of the shift on the radiation intensity introduces nonlinearity into the rate of the inter-subband absorption resulting in bistability and hysteresis of the resonant response. The hysteresis of the response explains the behavior in the regime of frequency modulation, which we observe for electrons on liquid $^3$He and which was previously seen for electrons on liquid $^4$He.

The microwave (MW) absorption resonance in 2D electrons bound to the surface of liquid 3He is studied at high MW powers. In our experiment, we induce quantum transitions between two lowest surface states of electrons by letting them interact with the resonant MW radiation. Under the conditions of the experiment, the resonant absorption induces strong heating of the electron system. The electron temperature can be accurately determined by measuring the variation of the electron magneto-resistivity at the resonance. Electron heating causes a shift in the resonance frequency, which is measured as a function of the electron temperature. The shift is compared with a theory that takes into account strong electron-electron correlation, and a reasonable agreement is found. When the shift exceeds the width of the absorption line, their emerges bistability of the nonlinear response and hysteresis. Our result demonstrate the occurrence of a new nonlinear optical effect due to strong correlations in the many-electron system on liquid helium.

Charge offsets and two-level fluctuators are common in single-electron transistors with a typical magnitude of |ΔQ|<0.1e. We present measurements in a 2e-periodic single-Cooper-pair transistor which exhibited hysteretic charge offsets close to 1e. The real-time capture and escape of individual electrons in metastable trapped states was measured at very low temperatures. This enabled the dynamics of the transitions to be investigated in detail, demonstrating thermal excitation to a hysteretic tunneling transition. We show that, allowing for the hysteresis, the metastable states are in thermal equilibrium with each other. The observed temperature dependence and hysteresis can be explained by the coupling of a two-level fluctuator to a quasiparticle trap.

We show that electrons on liquid helium display intrinsic bistability of resonant intersubband absorption. The bistability occurs for comparatively weak microwave power. The underlying giant nonlinearity of the many-electron response results from the interplay of the strong short-range electron correlations, the long relaxation time, and the multisubband character of the electron energy spectrum.

Metastable electron traps and two-level systems (TLSs) are common in solid-state devices and lead to background charge movement and charge noise in single-electron and single-Cooper-pair transistors. We present measurements of the real-time capture and escape of individual electrons in metastable trapped states at very low temperatures, leading to charge offsets close to 1e. The charge movement exhibits thermal excitation to a hysteretic tunneling transition. The temperature dependence and hysteresis can be explained by the coupling of a TLS to a quasiparticle trap.

Surface-state electrons on liquid helium, have been proposed as condensed matter qubits [1]. We have demonstrated that small numbers of electrons, including a single isolated electron, can be held in an electrostatic trap above the surface of superfluid helium [2] and individually detected using a superconducting single-electron transistor (SET). A new design for a quantum information processor, using an array of electron traps on liquid helium, has been fabricated on a Si wafer using a superconducting Al SET.

Conductivity measurements on three disc-shaped n-InSb samples were carried out in magnetic fields up to 70 kG at temperatures down to 40 mK and over a frequency range of 0–105 Hz. In the hopping-conduction region the a.c. and d.c. conductivities were found to scale according to:σ(ω, T)/σ(0, T) = f [AωT/σT(0, T)], where ~ωT and ~σT are normalized values and f is a universal function obtained by Summerfield. The parameter -log10 A is found to be 3·0±0·2, a value which is predicted by theory for some semiconductor materials with a constant density of states at the Fermi level.

We show that small numbers of electrons, including a single electron, can be held in a novel electrostatic trap above the surface of superfluid helium. A potential well is created using microfabricated electrodes in a 5 micron diameter pool of helium. Electrons are injected into the trap from an electron reservoir on a helium microchannel. They are individually detected using a superconducting single-electron transistor (SET) as an electrometer. A Coulomb staircase is observed as electrons leave the trap one-by-one until the trap is empty. A design for a scalable quantum information processor using arrays of electron traps is presented

Surface-state electrons on liquid helium, localised in quantum dots, have been proposed as condensed matter qubits. We now demonstrate experimentally that small numbers of electrons, including a single isolated electron, can be held in a novel electrostatic trap above the surface of superfluid helium. A potential well is created using microfabricated electrodes in a 5μm diameter pool of helium. Electrons are injected into the trap from an electron reservoir on a helium microchannel. They are individually detected using a superconducting single-electron transistor (SET) as an electrometer. A Coulomb staircase is observed as electrons leave the trap one-by-one until the trap is empty. A design for a prototype quantum information processor using an array of electron traps on liquid helium is presented.

Experiments are in progress to measure and control the quantum states of surface state electrons on liquid helium, both individually and in arrays, for potential use as qubits. This requires the fabrication of novel electronic devices using microstructured substrates, the excitation of Rydberg states using millimetric microwaves and the detection of individual electrons and their quantum states. This paper presents some preliminary experimental results.

A superconducting single electron transistor device has been designed and fabricated inside a ring which defines a shallow pool of liquid helium. The objective is to detect electrons trapped above the surface of the superfluid helium. Preliminary results are presented.

Conceptually simple experiments are always appealing. A classic example is the photoelectric effect—being the first demonstration of photons and the foundation of particle–wave duality and quantum physics. Light waves carry quantized energy and momentum. The analogous quantization of sound waves in condensed matter into phonons, with quanta of energy and momentum, is straightforward. A very direct confirmation of this quantization comes from the quantum evaporation of helium atoms from the surface of superfluid helium by experimentally generated phonons, or other ballistic excitations (see figure 1) in the liquid, in a one-to-one process of energy and momentum transfer from quanta to individual atoms. This beautiful idea was first proposed by Anderson in 1969 [1]. In 1978 Balibar et al [2] showed that evaporation of atoms by rotons in helium occurred, but they did not demonstrate the kinematics of the quantum process. This was done later by Adrian Wyatt and his group at Exeter University, UK in a remarkable series of experiments on the quantum evaporation of atoms from the superfluid ground state by elementary excitations in superfluid 4He (both rotons and phonons). Mark Brown and Adrian Wyatt gave a full account in 1990 [3], followed by a new analysis by Charles Williams in 1998 [4]. A key feature of this phenomenon is that the quantum evaporated atoms come directly from the Bose–Einstein condensate (BEC) of the superfluid, in which the atoms have zero momentum. Hence they do not contribute to the momentum of the evaporated atoms. Although only some 10 ± 1.5% of the helium atoms are in the zero-momentum and coherent BEC [5] (this is less than 100% because of interactions between the helium atoms) they dominate in the evaporated atomic beam as detected, which has a very narrow angular distribution. This gives direct evidence for the presence of the condensate at the surface of the superfluid helium [6]. Atoms evaporated from the non-condensate fraction would produce a very diffuse atomic beam and have not yet been observed. In this issue of J. Phys.: Condens. Matter [7], Mark Brown and Adrian Wyatt have now systematically explored the physics of the inverse effect of quantum condensation, first observed in 1977 [8]. An atom incident on the helium surface falls into the BEC and its kinetic energy and momentum, plus the binding energy, are transferred to a single quantum excitation. This simple idea reveals a wealth of experimental physics. A pulsed heater above the liquid produces a collimated beam of helium atoms, which impinge on the surface. The resultant excitations propagate through the superfluid at 80 mK and are detected by a superconducting Zn bolometer which measures the time-of-flight and the energy received. Three independent channels for energy transfer have been observed.

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.

We present measurements of the conduction of nondegenerate free electrons along a low-dimensional channel at low temperatures, using surface-state electrons on liquid helium in novel microelectronic devices. Above 1 K, the electrons form an ideal classical Drude conductor. Below 1 K, Coulomb interactions produce electronic spatial order, leading to strong non-Ohmic effects and negative differential conductivity. Evidence is presented for self-organized current filaments in the channel, created by a nonequilibrium phase transition. Periodic conductance oscillations suggest an anisotropic spatial order with lines of electrons along the channel edges.