(Last updated: Sep. 2, 2018)

My research interests include condensed-matter and quantum-optical theories. Specifically, I am interested in the interplay between local quantum systems and one or more reservoirs, which could be studied either in the context of open quantum systems, photon transport in the presence of strong light-matter interaction, or a more conventional setup such as a quantum dot coupled to metallic leads.

Project Ptychography:

Project Waveguide QED:

It was known that nonlinear elements, such as a two-level qubit, coupled to an infinite waveguide can create "two-photon bound states" by inelastic scattering, leading to photon correlations. Because of the 1D geometry, it is natural to ask what happens if a chain of qubits is cascaded along the waveguide. It turned out to be difficult mathematically, as multiple reflections between the qubits give rise to infinite number of poles in the scattering amplitudes. Using the Lippmann-Schwinger equation, we calculated the two-photon scattering wavefunction for a few (up to 10) identical, equally separated qubits in the waveguide, from which we obtained a variety of behaviors in photon correlation, including bunching and antibunching. The calculation was done analytically in the Markovian regime and numerically in the non-Markovian regime. We further generalized to the case of a semi-infinite waveguide, and found that the atom-mirror separation also plays an important role in modulating the decay rate. Moreover, we constructed the power spectrum using the scattering wavefunction, which reveals the effect of momentum redistribution due to inelastic scattering and allows the study of fluorescence (un-)quench. We found the equivalence between our scattering approach and the input-output theory widely used in quantum optics in the weak-pumping limit.

This project is also covered in our departmental newsletter.

Project Qauntum Monte Carlo:

For a quantum dot coupled to resistive metallic leads, a quantum phase transition could happen (at symmetric coupling) such that the a perfect transmission of electric current remains robust against the resistive environment. While a renormalization-group description was found for the spinless case, the extension to the spinful case remains challenging. We are working intensively on numerical computations using a continuous-time quantum Monte Carlo method in order to attack more complex scenarios, such as a spinful dot controlled by multiple electrostatic gates. Hopefully our numerical code will enable us to study how to stabilize the conductance (in the linear-response regime) for a complex structure immersed in a dissipative environment.