Jared H. Cole

Quantum phase transitions of light

The ability to conduct experiments at length scales and temperatures at which interesting and potentially useful quantum-mechanical phenomena emerge in condensed-matter or atomic systems is now commonplace. In optics, though, the weakness with which photons interact with each other makes exploring such behaviour more difficult. Here we describe an optical system that exhibits strongly correlated dynamics on a mesoscopic scale. By adding photons to a two-dimensional array of coupled optical cavities each containing a single two-level atom in the photon-blockade regime, we form dressed states, or polaritons, that are both long-lived and strongly interacting. Our results predict that at zero temperature the system will undergo a characteristic Mott insulator (excitations localized on each site) to superfluid (excitations delocalized across the lattice) quantum phase transition. Moreover, the ability to couple light to and from individual cavities of this system could be useful in the realization of tuneable quantum simulators and other quantum-mechanical devices.

Sensing of fluctuating nanoscale magnetic fields using nitrogen-vacancy centers in diamond

New magnetometry techniques based on nitrogen-vacancy (NV) defects in diamond allow for the detection of static (dc) and oscillatory (ac) nanoscopic magnetic fields, yet are limited in their ability to detect fields arising from randomly fluctuating (FC) environments. We show here that FC fields restrict dc and ac sensitivities and that probing the NV dephasing rate in a FC environment should permit the characterization of FC fields inaccessible to dc and ac techniques. FC sensitivities are shown to be comparable to those of ac magnetometry and require no additional experimental overhead or sample control.

Scanning quantum decoherence microscopy

The use of qubits as sensitive nanoscale magnetometers has been studied theoretically and recently demonstrated experimentally. In this paper we propose a new concept, in which a scanning two-state quantum system is used to probe a sample through the subtle effects of decoherence. Mapping both the Hamiltonian and decoherence properties of a qubit simultaneously provides a unique image of the magnetic (or electric) field properties at the nanoscale. The resulting images are sensitive to the temporal as well as spatial variation in the fields created by the sample. As examples we theoretically study two applications; one from condensed matter physics, the other biophysics. The individual components required to realize the simplest version of this device (characterization and measurement of qubits, nanoscale positioning) have already been demonstrated experimentally.

Identifying an experimental two-state Hamiltonian to arbitrary accuracy

Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on these parameters. This method requires only one measurement basis and the ability to initialize the system in some arbitrary state which is not an eigenstate of the Hamiltonian in question. The scaling of the uncertainty is studied for large numbers of measurements and found to be proportional to the reciprocal of the square root of the number of measurements.

Spatial coherent transport of interacting dilute Bose gases

Classically it is impossible to have transport without transit, i.e., if the points one, two and three lie sequentially along a path then an object moving from one to three must, at some point in time, be located at two. However, for a quantum particle in a three-well system it is possible to transport the particle between wells one and three such that the probability of finding it at any time in the classically accessible state in well two is negligible. We consider theoretically the analogous scenario for a Bose-Einstein condensate confined within a three well system. In particular, we predict the adiabatic transportation of an interacting Bose-Einstein condensate of 2000 Li atoms from well one to well three without transiting the allowed intermediate region. To an observer of this macroscopic quantum effect it would appear that, over a timescale of the order of 1s, the condensate had transported, but not transited, a macroscopic distance of ∼ 20μm between wells one and three.

Quantum phase transitions in photonic cavities with two-level systems

Systems of coupled photonic cavities have been predicted to exhibit quantum phase transitions by analogy with the Hubbard model. To this end, we have studied topologies of few (up to six) photonic cavities each containing a single two-level system. Quantum phase space diagrams are produced for these systems, and compared to mean-field results. We also consider finite effective temperature, and compare this to the notion of disorder. We find the extent of the Mott lobes shrink analogously to the conventional Bose-Hubbard model.

Spatial adiabatic passage in a realistic triple well structure

We investigate the evolution of an electron undergoing coherent tunneling via adiabatic passage (CTAP) using the solution of the one-dimensional Schrodinger equation in both space and time for a triple well potential. We find the eigenspectrum and complete time evolution for a range of different pulsing schemes. This also provides an example of a system that can be described with the tools from both quantum optics and condensed matter. We find that while the quantum optics description of the process captures most of the key physics, there are important effects that can only be correctly described by a more complete representation. This is an important point for applications such as quantum information processing or quantum control where it is common practice to use a reduced state space formulation of the quantum system in question.

Quantum-dot cellular automata using buried dopants

The use of buried dopants to construct quantum-dot cellular automata is investigated as an alternative to conventional electronic devices for information transport and elementary computation. This provides a limit in terms of miniaturization for this type of system as each potential well is formed by a single dopant atom. As an example, phosphorous donors in silicon are found to have good energy level separation with incoherent switching times of the order of microseconds. However, we also illustrate the possibility of ultrafast quantum coherent switching via adiabatic evolution. The switching speeds are numerically calculated and found to be tens of picoseconds or less for a single cell. The effect of decoherence is also simulated in the form of a dephasing process and limits are estimated for operation with finite dephasing. The advantages and limitations of this scheme over the more conventional quantum-dot based scheme are discussed. The use of a buried donor cellular automata system is also discussed as an architecture for testing several aspects of buried donor based quantum computing schemes.

Identifying a Two-State Hamiltonian in the Presence of Decoherence

Mapping the system evolution of a two-state system allows the determination of the effective system Hamiltonian directly. We show how this can be achieved even if the system is decohering appreciably over the observation time. A method to include various decoherence models is given and the limits of this technique are explored. This technique is applicable both to the problem of calibrating a control Hamiltonian for quantum computing applications and for precision experiments in two-state quantum systems. The accuracy of the results obtained with this technique are ultimately limited by the validity of the decoherence model used.

Subspace confinement: How good is your qubit?

The basic operating element of standard quantum computation is the qubit, an isolated two-level system that can be accurately controlled, initialized and measured. However, the majority of proposed physical architectures for quantum computation are built from systems that contain much more complicated Hilbert space structures. Hence, defining a qubit requires the identification of an appropriate controllable two-dimensional sub-system. This prompts the obvious question of how well a qubit, thus defined, is confined to this subspace, and whether we can experimentally quantify the potential leakage into states outside the qubit subspace. We demonstrate how subspace leakage can be characterized using minimal theoretical assumptions by examining the Fourier spectrum of the oscillation experiment.