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Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle quantum correlations in a large system in the presence of decoherence and external driving is especially topical. Still, scaling behaviour of dynamics and related emergent phenomena are not yet well understood. We investigate how the dynamics of a driven system of several quantum elements (e.g., qubits or Rydberg atoms) changes with increasing number of elements. Surprisingly, a two-element system exhibits chaotic behaviours. For larger system sizes a highly stochastic, far from equilibrium, {\em hyperchaotic} regime emerges. Its complexity systematically scales with the size of the system, proportionally to the number of elements. Finally, we demonstrate that these chaotic dynamics can be efficiently controlled by a periodic driving field. The insights provided by our results indicate the possibility of a reduced description for the behaviour of a large quantum system in terms of the transitions between its qualitatively different dynamical regimes, which are controlled by a relatively small number of parameters, and may prove useful in the design, characterization and control of large artificial quantum structures., 17 pages, 13 figures, 2 tables

The accurate control of magnetic fields is a cornerstone of multiple emerging quantum technologies. These technologies often require passive high permeability magnetic shielding and internal active field-generating coils to create their own bespoke magnetic field landscape. However, magnetic fields generated by coils are distorted by high permeability shielding, preventing the accurate and efficient generation of the desired field environment. Here, we design a cylindrical four-layer magnetic shield with an interior hybrid active-passive coil system that is explicitly optimised to include the electromagnetic coupling between the active and passive components. We use a combination of analytical methods and numerical simulations to determine the shield parameters - geometry, thickness, and access hole positions - to maximise the passive shielding efficiency and minimise the shield-induced Johnson noise and weight. Then, we apply an analytical formulation of the magnetic field, which accounts for the interaction with the magnetic shield, to design nine orthogonal hybrid active-passive field-generating coils inside the shield. The coils will be manufactured on thin low-via flex-PCBs near the shield's interior surface and generate three uniform fields and six gradient fields that deviate by less than 0.4% and 2%, respectively, over an internal cylindrical region extending over half the diameter and length of the innermost shield layer. These hybrid active-passive coils can accurately remove deviations in the background field or generate various complex magnetic field landscapes. Consequently, the hybrid shield provides an ideal platform for miniaturising and commercialising quantum technologies that require precisely-controlled magnetic fields within a low-noise environment.

Novel quantum technologies and devices place unprecedented demands on the performance of experimental components, while their widespread deployment beyond the laboratory necessitates increased robustness and fast, affordable production. We show how the use of additive manufacturing, together with mathematical optimization techniques and innovative designs, allows the production of compact, lightweight components with greatly enhanced performance. We use such components to produce a magneto-optical trap that captures $\sim 2 \times 10^8$ rubidium atoms, employing for this purpose a compact and highly stable device for spectroscopy and optical power distribution, optimized neodymium magnet arrays for magnetic field generation, and a lightweight, additively manufactured ultra-high vacuum chamber. We show how the use of additive manufacturing enables substantial weight reduction and stability enhancement, while also illustrating the transferability of our approach to experiments and devices across the quantum technology sector and beyond.

Hybrid magnetic shields with both active field generating components and high-permeability magnetic shielding are increasingly needed for a variety of technologies and experiments that require precision-controlled magnetic field environments. However, the fields generated by the active components interact with the passive magnetic shield, distorting the desired field profiles. Consequently, optimization of the active components needed to generate user-specified target fields must include coupling to the high-permeability passive components. Here, we consider the optimization of planar active systems, on which an arbitrary static current flows, coupled to a closed high-permeability cylindrical shield. We modify the Green's function for the magnetic vector potential to match boundary conditions on the shield's interior surface, enabling us to construct an inverse optimization problem to design planar coils that generate user-specified magnetic fields inside high-permeability shields. We validate our methodology by designing two bi-planar hybrid active--passive systems, which generate a constant transverse field, $\mathbf{B}=\mathbf{\hat{x}}$, and a linear field gradient, $\mathbf{B}=(-x~\mathbf{\hat{x}}-y~\mathbf{\hat{y}}+2z~\mathbf{\hat{z}})$, respectively. For both systems, the inverse-optimized magnetic field profiles agree well with forward numerical simulations. Our design methodology is accurate and flexible, facilitating the miniaturization of high-performance hybrid magnetic field generating technologies with strict design constraints and spatial limitations., Comment: 24 pages, 10 figures

We show that the performance and functionality of atom-chips can be transformed by using graphene-based van der Waals heterostructures to overcome present limitations on the lifetime of the trapped atom cloud and on its proximity to the chip surface. Our analysis involves Green-function calculations of the thermal (Johnson) noise and Casimir-Polder atom-surface attraction produced by the atom-chip. This enables us to determine the lifetime limitations produced by spin-flip, tunneling and three-body collisional losses. Compared with atom-chips that use thick metallic conductors and substrates, atom-chip structures based on two-dimensional materials reduce the minimum attainable atom-surface separation to a few 100 nm and increase the lifetimes of the trapped atom clouds by orders of magnitude so that they are limited only by the quality of the background vacuum. We predict that atom-chips with two-dimensional conductors will also reduce spatial fluctuations in the trapping potential originating from imperfections in the conductor patterns. These advantages will enhance the performance of atom-chips for quantum sensing applications and for fundamental studies of complex quantum systems., 22 pages, 14 figures

Magnetically-sensitive experiments and newly-developed quantum technologies with integrated high-permeability magnetic shields require increasing control of their magnetic field environment and reductions in size, weight, power and cost. However, magnetic fields generated by active components are distorted by high-permeability magnetic shielding, particularly when they are close to the shield's surface. Here, we present an efficient design methodology for creating desired static magnetic field profiles by using discrete coils electromagnetically-coupled to a cylindrical passive magnetic shield. We utilize a modified Green's function solution that accounts for the interior boundary conditions on a closed finite-length high-permeability cylindrical magnetic shield, and determine simplified expressions when a cylindrical coil approaches the interior surface of the shield. We use an analytic formulation of simple discrete building blocks to provide a complete discrete coil basis to generate any physically-attainable magnetic field inside the shield. We then use a genetic algorithm to find optimized discrete coil structures composed of this basis. We use our methodology to generate an improved linear axial gradient field, $\mathrm{d}B_z/\mathrm{d}z$, and transverse bias field, $B_x$. These optimized structures increase, by a factor of seven and three compared to the standard configurations, the volume in which the desired and achieved fields agree within $1\%$ accuracy, respectively. This coil design method can be used to optimize active--passive magnetic field shaping systems that are compact and simple to manufacture, enabling accurate magnetic field control in spatially-confined experiments at low cost., Comment: The authors M. Packer and P. J. Hobson have contributed equally to this work. 24 pages, 16 figures

Magnetic shields that use both active and passive components to enable the generation of a tailored low-field environment are required for many applications in science, engineering, and medical imaging. Until now, accurate field nulling, or field generation, has only been possible over a small fraction of the overall volume of the shield. This is due to the interaction between the active field-generating components and the surrounding high-permeability passive shielding material. In this paper, we formulate the interaction between an arbitrary static current flow on a cylinder and an exterior closed high-permeability cylinder. We modify the Green's function for the magnetic vector potential and match boundary conditions on the shield's interior surface to calculate the total magnetic field generated by the system. We cast this formulation into an inverse optimization problem to design active--passive magnetic field shaping systems that accurately generate any physical static magnetic field in the interior of a closed cylindrical passive shield. We illustrate this method by designing hybrid systems that generate a range of magnetic field profiles to high accuracy over large interior volumes, and simulate them in real-world shields whose passive components have finite permeability, thickness, and axial entry holes. Our optimization procedure can be adapted to design active--passive magnetic field shaping systems that accurately generate any physical user-specified static magnetic field in the interior of a closed cylindrical shield of any length, enabling the development and miniaturization of systems that require accurate magnetic shielding and control., 22 pages, 9 figures, 1 table

The capabilities of a radio-frequency atomic magnetometer for object detection based on magnetic induction tomography are explored. The determination of object orientation is demonstrated by utilizing the measurement geometry. The self-compensation configuration of the atomic magnetometer is implemented to address the issue of saturation of the sensor response by the radio-frequency primary field that generates the object signature. Three methods of "covert" detection are investigated as a testbed for exploring the functionalities of this sensor, where (1) the operational frequency of the sensor is continuously changed, (2) the primary field has non-monochromatic frequency distribution, and (3) the sensor operates in the so-called spin maser mode. The results of the measurements are also discussed in terms of possible magnetic field communication.

We investigate the effect of hypersonic (> 1 GHz) acoustic phonon wavepackets on electron transport in a semiconductor superlattice. Our quantum mechanical simulations demonstrate that a GHz train of picosecond deformation strain pulses propagating through a superlattice can generate current oscillations whose frequency is several times higher than that of the strain pulse train. The shape and polarity of the calculated current pulses agree well with experimentally measured electric signals. The calculations also explain and accurately reproduce the measured variation of the induced current pulse magnitude with the strain pulse amplitude and applied bias voltage. Our results open a route to developing acoustically-driven semiconductor superlattices as sources of millimetre and sub-millimetre electromagnetic waves., 5 pages, 4 figures, submitted to Phys Rev App

Recent advances in the preparation, control and measurement of atomic gases have led to new insights into the quantum world and unprecedented metrological sensitivities, e.g. in measuring gravitational forces and magnetic fields. The full potential of applying such capabilities to areas as diverse as biomedical imaging, non-invasive underground mapping, and GPS-free navigation can only be realised with the scalable production of efficient, robust and portable devices. We introduce additive manufacturing as a production technique of quantum device components with unrivalled design freedom and rapid prototyping. This provides a step change in efficiency, compactness and facilitates systems integration. As a demonstrator we present an ultrahigh vacuum compatible ultracold atom source dissipating less than ten milliwatts of electrical power during field generation to produce large samples of cold rubidium gases. This disruptive technology opens the door to drastically improved integrated structures, which will further reduce size and assembly complexity in scalable series manufacture of bespoke portable quantum devices.

Surface plasmon resonance (SPR) at planar metal/dielectric interfaces and localised SPR (LSPR) for metal nanoparticles have both been extensively studied, but it is less clear what happens to the optical properties of surface plasmon-polaritons (SPPs) at the micrometer scale. This paper characterises the angular responses of microscale gold patterns on a glass substrate using an SPR imaging configuration using a high numerical aperture objective lens. The potential use for biosensing is also discussed. The propagation length of a SPP equals approximately 10 μm, so the geometries that are investigated are 10 × 16, 10 × 10, 6 × 16, and 6 × 6 μm sized rectangles with 2 μm spacings. The gold patterns are photolithographically produced using an image reversal process. Bright-field microscopy is used to investigate their morphology and stylus profilometry is used to check the gold thickness. The SPR responses were compared to planar gold film to see if they were characteristic and confirm the relation to SPR. All the gold microstructures present plasmonic properties. SPR dips are observed for all samples, however, they are not as sensitive and are wider than that of planar gold film. This phenomenon becomes more pronounced as the length of the gold structure decreases, because of the spatial constriction of the propagating SPP. The process suggests that the SPR technique can be successfully implemented to detect individual action potentials. Further work is required in order to achieve a reliable process and investigate the capabilities and sensitivity of the proposed technique.

The effect of the bandgap width between the first and second energy minibands on the charge transport in a semiconducting superlattice to which electric and tilted magnetic fields are applied is studied theoretically. The time dependences of the current passing through the superlattice are calculated, and the dependences of the amplitude and frequency of electric current oscillations on the applied voltage are constructed. It is found that the interminiband electron tunneling facilitates a decrease in the amplitude of current oscillations, but simultaneously increases their frequency.

We introduce and investigate a system that uses temporal resonance-induced phase space pathways to create strong coupling between an atomic Bose-Einstein condensate and a traveling optical lattice potential. We show that these pathways thread both the classical and quantum phase space of the atom cloud, even when the optical lattice potential is arbitrarily weak. The topology of the pathways, which form web-like patterns, can by controled by changing the amplitude and period of the optical lattice. In turn, this control can be used to increase and limit the BEC's center-of-mass kinetic energy to pre-specified values. Surprisingly, the strength of the atom-lattice interaction and resulting BEC heating of the center-of-mass motion is enhanced by the repulsive inter-atomic interactions., 8 pages, 7 figures

We study high-frequency generation in a system of electromagnetically coupled semiconductor superlattices fabricated on the same doped substrate. Applying a bias voltage to a single superlattice generates high-frequency current oscillations. We demonstrate that within a certain range of the applied voltage, the current oscillations within the superlattices can be self-synchronized, which leads to a dramatic rise in the generated microwave power. These results, which are in good agreement with our numerical model, open a promising practical route towards the design of high-power miniature microwave generators.

Superfluidity and superconductivity have been studied widely since the last century in many different contexts ranging from nuclear matter to atomic quantum gases. The rigidity of these systems with respect to external perturbations results in frictionless motion for superfluids and resistance-free electric current in superconductors. This peculiar behaviour is lost when external perturbations overcome a critical threshold, i.e. above a critical magnetic field or a critical current for superconductors. In superfluids, such as liquid helium or ultracold gases, the corresponding quantities are critical rotation rate and critical velocity, respectively. Enhancing the critical values is of great fundamental and practical value. Here we demonstrate that superfluidity can be achieved for flow above the critical velocity through quantum interference induced resonances. This has far reaching consequences for the fundamental understanding of superfluidity and superconductivity and opens up new application possibilities in quantum metrology, e.g. in rotation sensing., 6 pages, 4 figures

The mechanisms of transitions between different regimes of current oscillations in a semiconductor superlattice in the presence of a tilted magnetic field at various temperatures have been studied. At relatively low temperatures, an increase in the applied voltage leads to a period-doubling bifurcation that causes a change in the dynamic regime. At increased temperatures, the transition takes place with the quenching of current oscillations.

The UK National Quantum Technology Hub in Sensors and Metrology is one of four flagship initiatives in the UK National of Quantum Technology Program. As part of a 20-year vision it translates laboratory demonstrations to deployable practical devices, with game-changing miniaturized components and prototypes that transform the state-of-the-art for quantum sensors and metrology. It brings together experts from the Universities of Birmingham, Glasgow, Nottingham, Southampton, Strathclyde and Sussex, NPL and currently links to over 15 leading international academic institutions and over 70 companies to build the supply chains and routes to market needed to bring 10–1000x improvements in sensing applications. It seeks, and is open to, additional partners for new application development and creates a point of easy open access to the facilities and supply chains that it stimulates or nurtures.

The space-time dynamics of electron domains in a semiconductor superlattice is studied in a tilted magnetic field with regard to the effect of temperature. It is shown that an increase in temperature substantially changes the space-time dynamics of the system. This leads to a decrease in the frequency and amplitude of oscillations of a current flowing through the semiconductor superlattice. The quenching of oscillations is observed, which is attributed to the change in the drift velocity as a function of electric-field strength under the variation of temperature.

We observe a series of sharp resonant features in the differential conductance of graphene-hexagonal boron nitride-graphene tunnel transistors over a wide range of bias voltages between 10 and 200 mV. We attribute them to electron tunneling assisted by the emission of phonons of well-defined energy. The bias voltages at which they occur are insensitive to the applied gate voltage and hence independent of the carrier densities in the graphene electrodes, so plasmonic effects can be ruled out. The phonon energies corresponding to the resonances are compared with the lattice dispersion curves of graphene-boron nitride heterostructures and are close to peaks in the single phonon density of states.

Magneto-conductance fluctuations serve as the traditional method for investigating the dynamics of electrons as they flow through solid-state materials. Generated by electron wave interference, their spectral content is critically sensitive to the precise scattering configurations in the material. In this paper, we exploit this sensitivity to study the electron dynamics in the diffusive regime of semiconductors where the dynamics are determined by material-induced scattering. We show that the spectral content of the fluctuations measured on diffusive n + GaAs wires and quasi-ballistic AlGaAs/GaAs wires follow a fractal scaling behaviour similar to that previously observed in ballistic semiconductors. We present an interpretation based on chaotic dynamics generated by the material-induced disorder.

We show that the reflection of quantum-mechanical waves from semiconductor surfaces creates new regimes of nonlinear dynamics, which offer sensitive control of electrons and ultra-cold atoms. For electrons in superlattices, comprising alternating layers of different semiconductor materials, multiple reflections of electron waves from the layer interfaces induce a unique type of chaotic electron motion when a bias voltage and tilted magnetic field are applied. Changing the field parameters switches the chaos on and off abruptly, thus producing a sharp increase in the measured current flow by creating unbounded electron orbits. These orbits correspond to either intricate web patterns or attractors in phase space depending on the electron decoherence rate. We show that related dynamics provide a mechanism for controlling the transmission of electromagnetic waves through spatially-modulated photonic crystals. Finally, we consider the quantum dynamics of a Bose-Einstein condensate, comprising 120,000 rubidium atoms cooled to 10 nK, incident on a stadium billiard etched in a room-temperature silicon surface. Despite the huge temperature difference between the condensate and the billiard, quantum-mechanical reflection can shield the cold atoms from the disruptive influence of the surface, thus enabling the billiard to imprint signatures of single-particle classical trajectories in the collective motion of the reflected atom cloud.

A new class of multilayered functional materials has recently emerged in which the component atomic layers are held together by weak van der Waals forces that preserve the structural integrity and physical properties of each layer. An exemplar of such a structure is a transistor device in which relativistic Dirac Fermions can resonantly tunnel through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. An applied magnetic field quantises graphene's gapless conduction and valence band states into discrete Landau levels, allowing us to resolve individual inter-Landau level transitions and thereby demonstrate that the energy, momentum and chiral properties of the electrons are conserved in the tunnelling process. We also demonstrate that the change in the semiclassical cyclotron trajectories, following a tunnelling event, is a form of Klein tunnelling for inter-layer transitions., in Nature Physics (2015)

We examine the feasibility of amplification of the electromagnetic signal in semiconductor superlattice by moving charge domains, which are generated in superlattice by applied DC bias. We show that an external resonator connected to the semiconductor superlattice significantly broadens the frequency range of amplified signals to the higher harmonics of domain transient frequency. These promising results open the way to use semiconductor superlattices as the efficient sub-THz/THz amplifiers.

We assess the potential of two-terminal graphene-hexagonal boron nitride-graphene resonant tunneling diodes as high-frequency oscillators, using self-consistent quantum transport and electrostatic simulations to determine the time-dependent response of the diodes in a resonant circuit. We quantify how the frequency and power of the current oscillations depend on the diode and circuit parameters including the doping of the graphene electrodes, device geometry, alignment of the graphene lattices, and the circuit impedances. Our results indicate that current oscillations with frequencies of up to several hundred GHz should be achievable.

is an integer, the electron orbits change fromlocalised Bloch-like trajectories to unbounded stochastic orbits, which difiuserapidly through intricate web patterns in phase space. To quantify how thesewebs afiect electron transport, we make drift-difiusion calculations of thecurrent{voltage curves including the efiects of space-charge build up. Whenthe magnetic fleld is tilted, our simulations reveal a large resonant peak,which originates from stochastic delocalisation of the electron orbits. Weshow that the corresponding quantised eigenstates change discontinuouslyfrom a highly localised character when the system is ofi resonance to a fullydelocalised form when the resonance condition is satisfled.PACS numbers: 73.20.At, 73.21.Cd

Chaotic electron transport has been explored in a variety of semiconductor structures in which the transition to chaos occurs by the gradual and progressive destruction of stable orbits in response to an increasing perturbation. There is also a much rarer type of chaos, known as non-KAM dynamics, which switches on and off abruptly when the temporal frequency of the perturbation reaches certain critical values. This type of chaotic motion is of great interest due to diverse applications in the theory of plasma physics, tokamak fusion, turbulent fluid dynamics, ion traps, and quasicrystals, but has not yet been realized in experiment. Here, we show that electrons in a superlattice miniband with a tilted magnetic field provide an experimentally-accessible non-KAM system and, moreover, that this unusual type of chaotic dynamics can produce strong resonant enhancement of the electron drift velocity. The onset of chaos is characterized by the formation of intricate “stochastic web” patterns in the electron phase space. These webs delocalize the electron orbits, thereby generating strong resonant peaks in our calculated drift velocity versus electric field characteristics.

We present measurements of the potential profile of etched GaInAs/InP billiards and show that their energy gradients are an order of magnitude steeper than those of surface-gated GaAs/AlGaAs billiards. Previously observed in GaAs/AlGaAs billiards, fractal conductance fluctuations are predicted to be critically sensitive to the billiard profile. Here we show that, despite the increase in energy gradient, the fractal conductance fluctuations persist in the harder GaInAs/InP billiards. (C) 2004 Elsevier Ltd. All rights reserved.

We present experimental results demonstrating that fractal conductance fluctuations are remarkably robust to deviations from the semiclassical conduction regime. We find that the fractal dimension depends solely on an empirical parameter that quantifies the resolution of the billiard's discrete energy level spectrum. Non-fractal fluctuations are obtained only in the extreme classical and quantum-mechanical conduction regimes.

We present a comprehensive study of the dependence of fractal conductance fluctuations (FCF) on semiconductor billiard parameters. We find that the fractal dimension depends solely on an empirical parameter that quantifies the resolution of the discrete energy level spectrum of the billiard. We have also investigated the effect of profile softness using billiards formed in a double two-dimensional electron gas heterostructure and find that FCF are robust to the changes in profile softness achieved.

We have developed and investigated a double-2DEG billiard to study the dependence of fractal conductance fluctuations on the soft-wall potential profile in semiconductor billiards. We use numerical modeling to establish how the profile differs between the billiards. We present preliminary results showing that the changes in profile modify the fractal dimension rather than suppress the fractal behavior, and that the fractal dimension depends inversely on the softness of the potential profile.

We investigate the effects of a linear resonator on the high-frequency dynamics of electrons in devices exhibiting negative differential conductance. We show that the resonator strongly affects both the dc and ac transport characteristics of the device, inducing quasiperiodic and high-frequency chaotic current oscillations. The theoretical findings are confirmed by experimental measurements of a GaAs/AlAs miniband semiconductor superlattice coupled to a linear microstrip resonator. Our results are applicable to other active solid state devices and provide a generic approach for developing modern chaos-based high-frequency technologies including broadband chaotic wireless communication and superfast random-number generation.

The quantized states of a 60 nm wide potential well in a large tilted magnetic field are investigated using scaled field resonant tunnelling spectroscopy. In contrast to previous experiments on this type of system, the tunnelling characteristics are measured by changing both the magnetic field strength B and the applied bias voltage V such that V/B2 is approximately constant. This ensures that the classical phase space for electrons in the potential well has the same mixed stable-chaotic character for all fields. As a consequence of this scaling, each closed orbit in the potential well produces many periodic resonant peaks in plots of d2I/dB2 versus B. This type of scaled field experiment can be used to probe quantum states corresponding to dynamical regimes which are inaccessible to fixed field resonant tunnelling studies. We also consider analogies between the electron orbits and light rays in gradient refractive index lenses.

We report a new type of quantum chaotic system in which the classical Hamiltonian originates from the intrinsically quantum mechanical nature of the device. The system is a semiconductor superlattice in a magnetic field. The energy–momentum dispersion curves can be used to calculate semi- classical orbits for electrons confined to a single miniband. When a magnetic field is applied along the superlattice axis (x-direction), the electrons perform Bloch oscillations along the axis with cyclotron motion in the orthogonal plane. But when the magnetic field is tilted away from the x-direction, the orbits are chaotic, and have a spatial width along the superlattice axis, which is much larger than the amplitude of the Bloch oscillations. This is because the tilted field transfers momentum between the x- and z-directions, thereby delocalizing the electron path. This type of chaotic dynamics is fundamentally different to that identified in our previous studies of double–barrier resonant tunneling diodes. We investigate the relation between the orbits of the effective Hamiltonian, and the quantum states of the superlattice. In the regime of strong chaos, the wave functions have a highly diffuse structure which extends across many periods of the superlattice, just like the corresponding classical orbits. This chaos-induced delocalization increases the current flow through real devices. By contrast, in the stable domain the electron orbits remain localized along the paths of particular quasi-periodic orbits. We use theoretical and experimental current–voltage curves to show how the onset of chaos manifests itself in the transport properties of two- and three-terminal superlattice structures, and identify current oscillations associated with classical resonances. We also consider analogies with ultra-cold atoms in an optical lattice with a tilted harmonic trap.

We show how ultracold (sub-µK temperature) atoms in a one-dimensional periodic optical potential with a harmonic trap can provide a new quantum chaotic system that is accessible to experiment. Provided that the harmonic potential varies slowly over a lattice period, the optical lattice has well defined energy bands. The energy-wavevector dispersion curves define an effective Hamiltonian that can be used to calculate classical orbits for atoms confined to a single band. We show that tilting the harmonic trap relative to the optical lattice induces a controllable transition from stable regular motion to classical chaos. The onset of chaos strongly delocalizes the atom orbits and should be manifest in both the classical and quantum properties of the trapped atoms. We also consider how the transition to chaos might affect the collective time-dependent dynamics of interacting atoms in Bose-Einstein condensates.

Fractal behaviour in the magneto-conductance fluctuations of mesoscopic systems has been predicted using semiclassical theory and observed experimentally in semiconductor billiards. Surface-gate billiards provide an ideal environment for investigations of fractal behaviour due to the ease with which parameters in the experimental system can be tuned. In this study we vary temperature and billiard size to investigate the classical and quantum limits of the semiclassical theory for fractal magneto-conductance fluctuations.

We introduce semiconductor superlattices as a new type of quantum chaotic system that is accessible to experiment. In contrast to previous physical systems that have been used to study quantum chaos, the classical Hamiltonian for the superlattices has an intrinsically quantum–mechanical origin. For low electric fields, superlattices have well-defined minibands which originate from the quantum–mechanical coupling of electron states in a periodic array of potential wells. The energy-wave-vector dispersion curves define an effective Hamiltonian that can be used to calculate semiclassical orbits for electrons confined to a single miniband. We show that applying a tilted magnetic field induces a controllable transition from stable regular motion to strong classical chaos. The onset of chaos delocalizes both the classical orbits and the corresponding quantum wave functions, and is therefore expected to produce a sharp increase in the current flow measured in electron transport experiments. We show that magnetically confined atoms in a periodic optical potential exhibit similar chaotic dynamics at ultra-low (μK) temperatures.

We report quantum-mechanical calculations which replicate the self-similar magnetoconductance fluctuations observed in recent experiments on semiconductor Sinai billiards. We interpret these fluctuations by considering the mixed stable-chaotic classical dynamics of electrons in the billiard. In particular, we show that the fluctuation patterns are dominated by individual stable orbits. The scaling characteristics of the self-similar fluctuations depend on the geometry of the associated stable orbit. We find that our analysis is insensitive to the details of the potential landscape, and is applicable to real devices with a wide range of soft-wall profiles. We show that our analysis also provides a possible explanation for the distinct series of magnetoconductance fluctuations observed in recent experiments on carbon nanotubes.

Experimental and theoretical studies of electron transport in a resonant tunnelling diode with a tilted magnetic field are reported. We map the transition to chaotic dynamics for electrons injected into the potential well from an emitter accumulation layer. In the regime of mixed stable-chaotic electron dynamics, we have identified a stable-orbit trifurcation that leads to a sudden three-fold reduction in the voltage spacing of resonant peaks in the calculated and measured current–voltage curves. We explain this effect by considering how the dynamical properties of the stable orbits affect the quantized states of the potential well.

We present a model for the self-similar magneto-conductance recently observed in the low-temperature measurement of a semiconductor Sinai billiard. To model the self-similar behaviour, we investigate the scaling properties observed over more than three orders of magnitude in magnetic field. The magneto-conductance is found to be composed of a summation of damped cosines scaled according to a Weierstrass function—a known generator of self-similar behaviour. Our preliminary model, based on a single hierarchy of oscillations with magnetic flux periods of h/2e, provides a close match to the experimental data. However, a refined model featuring co-existing h/e and h/2e hierarchies matches the features of the data with remarkable accuracy.

The semiclassical motion of an electron along the axis of a superlattice may be calculated from the miniband dispersion curve. Under a weak electric field the electron executes Bloch oscillations which confines the motion along the superlattice axis. When a magnetic field, tilted with respect to the superlattice axis, is applied the electron orbits become chaotic. The onset of chaos is characterised by a complex mixed stable-chaotic phase space and an extension of the orbital trajectories along the superlattice axis. This delocalisation of the orbits is also reflected in the quantum eigenstates of the system some of which show well-defined patterns of high probability density whose shapes resemble certain semiclassical orbits. This suggests that the onset of chaos will be manifest in electron transport through a finite superlattice. We also propose that these phenomena may be observable in the motion of trapped ultra-cold atoms in an optically induced superlattice potential and magnetic quadrupole potential whose axis is tilted relative to the superlattice axis.

We show that a phonon wave propagating through a semiconductor superlattice can induce a charge current even when no static electric field is applied. When the energy amplitude of the phonon wave is less than the width of the lowest superlattice miniband, we find strong resonant enhancement of electron transport, accompanied by very high frequency oscillations of the electron orbits. In this regime, the phonon wave drags the electrons through the superlattice, causing them to undergo quasi-periodic trajectories with a single dominant temporal frequency several orders of magnitude higher than that of the phonon deformation wave itself. This transformation of GHz frequency wave motion into highly coherent THz frequency electron dynamics provides a mechanism for frequency up-conversion, with a multiplication factor of ~20 in our present samples. For phonon wave amplitudes higher than the miniband width, the electrons perform Bloch-like oscillations, which dramatically suppresses transport.

We show how semiconductor superlattices can be used to provide a new type of quantum chaotic system that is accessible to experiment. When a magnetic field is tilted relative to the superlattice axis, the semiclassical orbits of electrons confined to a single miniband undergo a controllable transition from stable Bloch oscillations to chaotic orbits. The onset of chaos delocalizes the electron paths and generates complex trajectories that extend across many periods of the superlattice. We show that the chaotic motion has a fundamentally different origin to that reported for previous semiconductor structures.

Theoretical and experimental investigations are made of the dynamical behaviour of hot electrons injected into the quantum well of a resonant tunnelling diode in an obliquely oriented magnetic field. The transition to chaos is mapped as a function of the applied voltage and magnetic field. A region of mixed stable–chaotic dynamics is identified and associated with a stable-orbit trifurcation, which leads to a reduction in the voltage spacing of the resonant peaks in the tunnel current by a factor of 1 3 . The quantum eigenfunctions associated with both stable and unstable periodic orbits are calculated and related to the current–voltage characteristics.