Quantum & Condensed Matter Physics Projects

An Analog Circuits Approach to Quantum Systems

This project maps the stochastic and deterministic dynamics of open and closed quantum systems to analog circuit architectures and motifs. Such motifs may then be used to both map quantum systems to analog supercomputing chips, and to design novel quantum circuits. Many common circuit themes in analog and quantum computation include noise and thermodynamics, fault tolerance, feedback control, back action and loading, entanglement and correlation, precision measurement,  nonlinear dynamics, robustness-efficiency tradeoffs, scalability,  and hybrid quantum-classical operation.

FACULTY CONTACT: Rahul Sarpeshkar

Quantum Simulation with Cold Atoms in Engineered Optical Potentials

Many-body quantum systems can be very difficult to handle theoretically, and in some important cases the true nature of the phase diagram is not yet accurately known. One possible path to gain deeper understanding of these incredibly rich physical systems is to engineer a "synthetic" many body quantum system that maps onto a particular system of interest, but has more conveniently tunable properties. Ultracold atoms in engineered optical potentials are one platform for such an approach. We are developing optical trapping and manipulation techniques to create (and examine the properties of) various strongly correlated and "topological" quantum phases of matter.


Symmetry Breaking and Critical Scaling in Ultracold Quantum Gases

Driving a physical system abruptly through a continuous phase transition leads to a variety of interesting physical phenomena, including spontaneous formation of topological defects such as solitons, vortex lines, and monopoles. This is a universal phenomenon which is relevant to systems as diverse as ultra-cold quantum fluids and the cooling of the universe shortly after a `hot big bang'. The critical behavior of these systems is not determined by local dynamics, but rather by universal scaling laws arising from key global parameters (e.g. dimensionality, spin degrees of freedom, interaction range) . Laboratory tests of of these critical scaling theories have to date proven to be challenging, with some limited success. We are using new techniques for controlling ultracold (Fermi and Bose) gases to try to more rigorously test some of these critical scaling predictions.


Topological Quantum Matter

Topological phases of matter are distinguished by a form of quantum order that cannot be characterized in terms of any local order parameter. A most striking manifestation of topological order is the emergence of topologically protected zero-energy boundary modes that are otherwise not realized in Nature. For a topological superconductor, in particular, such emergent quasi-particles coincide with their own anti-particles, naturally embodying elusive quantum objects known as "Majorana fermions". We are investigating new routes for realizing topological superconductors in condensed-matter systems, with the goals of both elucidating fundamental physical aspects of Majorana fermions and their possible significance for topologically robust qubit implementations.


Many-Body Quantum Chaos and Quantum Thermodynamics

Understanding and justifying the emergence of equilibrium behavior in generic, non-integrable many-body quantum systems is a longstanding challenge at the very heart of statistical mechanics. We are exploring how concepts and tools from quantum information theory may be used to build a consistent theoretical framework for describing ergodicity and mixing properties in many-body quantum systems that lack a natural classical counterpart, and to characterize distinctive aspects of complex quantum dynamics. Beside their foundational implications, these studies are directly relevant to ongoing experiments on quantum chaos and thermalization dynamics in Ramanathan's group.


Entanglement and Quantum Correlations

Entanglement provides a distinctively quantum type of correlation that has no analogue in classical statistical mechanics. Despite much progress, a satisfactory understanding of the nature and properties of quantum correlations in composite quantum systems, and the extent to which different kinds of correlations may be a resource for quantum information tasks is far from being reached. We are exploring fundamental aspects of quantum correlations, including a framework for describing limitations in "sharing" and "joining" quantum states and channels, as well as for generalizing entanglement theory beyond its standard subsystem-based setting.


Dynamics and Control of Open Quantum Systems

Precisely characterizing and controlling the states and dynamics of realistic open quantum systems is a fundamental challenge across quantum science and engineering, and a prerequisite for harnessing the potential of quantum information processing. We are investigating a range of problems in quantum control from both a general system-theoretic perspective as well as in collaboration with experimentalists working on trapped-ion and solid-state qubit implementations. Current projects include dynamical decoherence suppression and noise identification in multi-qubit systems, quantum control using engineered dissipation, and fundamental limits to cooling.


Readout of Spin Qubits in Si/SiGe Quantum Dots Using a Cavity Embedded Cooper Pair Transistor

Spin qubits in Si/SiGe quantum dots are expected to enjoy very long coherence times, due to the weak interaction of the spins with their environment. The same weakness of interaction makes it difficult to determine the state of the qubits, and to transfer the quantum information they contain to other devices. In this project, we plan to use a superconducting device, the Cooper pair transistor, as a charge-tunable inductance that influences the resonant frequency of a superconducting microwave cavity. The expected interaction between photons and spins is so strong that we should be able to read out the state of a qubit with a single photon. Conversely, we should be able to use a single photon to manipulate the state of a qubit. This research is performed in collaboration with the semiconductor qubit group at the University of Wisconsin.


Measurement of Single Phonons with Single Photons

There has been great recent progress in controlling the quantum behavior of nanomechanical resonators. In this project, we aim to extend such control to the strongly quantum regime in which a single photon can be used to either read out or act back on a single phonon. To do so, we will use a superconducting device, the Cooper pair transistor, as a charge-tunable inductance embedded in a superconducting microwave cavity. By coupling the transistor to a nanomechanical resonator, we plan to use resonator motion at the level of a single phonon to shift the resonant frequency of the cavity. This capability should allow us to investigate strongly non-linear quantum interactions of light with matter, with implications for quantum measurement and information science. Our group collaborates closely with the group of Miles Blencowe on this project.


Generation of Quantum States of Light with a Josephson Laser

Quantum states of light are a topic of considerable current interest, and may lead to use of continuous variables for quantum information processing, as well as to quantum-enhanced measurements. Ideally, one would like to be able to generate such states simply, and to have the states contain large numbers of photons. We have recently developed a device, the cavity-embedded Cooper pair transistor, that uses the ac Josephson effect to inject large numbers of microwave photons into a cavity. The photons induce stimulated emission of additional photons from the transistor, making the device a single-emitter Josephson laser. Our efforts are now focused on determining the quantum state of the photons in the cavity, and on studying the quantum dynamics of this strongly non-linear system. Our group collaborates closely with the group of Miles Blencowe on this project.