Session S6: Solid State Qubits, Resonators, and Quantum Optics

Quantum optics with superconducting qubits in the dispersive limit

Several recent experiments have demonstrated that superconducting circuits are ideal systems for the study of quantum mechanical effects on large scale and promising candidates for quantum computation. It was recently proposed [1] and experimentally demonstrated [2,3] that superconducting circuits fabricated inside a high quality on-chip transmission line resonator can be used to study solid-state analogs of quantum optics experiments and, in particular, to reach the strong-coupling regime of cavity quantum electrodynamics (CQED). In this talk, this theoretical proposal will be reviewed and experimental results in the dispersive regime will be presented, for both the time and frequency domain. Results in the time domain show our ability to coherently control the state of the qubit, while detailed analysis of the frequency domain results yields insights into the measurement process and its backaction.\par [1] A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin and R. J. Schoelkopf, Phys. Rev. A {\bf 69}, 062320 (2004).\par [2] A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin and R. J. Schoelkopf, Nature {\bf 431}, 162 (2004).\par [3] D. Schuster, A. Wallraff, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. M. Girvin and R. J. Schoelkopf, cond-mat/0408367.   

Mesoscopic cavity quantum electrodynamics with atomic systems and quantum dots

We discuss electrodynamic techniques for strong, coherent coupling between spatially separated atoms or quantum dots on a microchip. These techniques are based on capacitive interactions between the electron charge and a superconducting transmission line resonator operating in microwave domain, and are analogous to cavity quantum electrodynamics. In the case of isolated neutral atoms, the coupling is achieved by exciting atoms trapped above the surface of a superconducting transmission line into Rydberg states with large electric dipole moments that induce voltage fluctuations in the resonator. In the case of quantum dots, interactions between the resonator and the electron charge may be exploited to couple spatially separated electron-spin states while only virtually populating fast-decaying superpositions of charge states. We discuss potential applications of such electrodynamic coupling for a long-range interaction between a variety of spatially separated quantum systems, for entangling isolated neutral atoms separated by millimeters, or for mapping the quantum states of a solid-state device onto atomic or photonic states. Finally, we discuss prospects for extending these on-chip cavity QED techniques into the optical domain.   

Strong coupling between a quantum dot and a photonic crystal nanocavity

We report the observation of vacuum Rabi splitting (true strong coupling) between a single InAs quantum dot and a photonic crystal nanocavity.$^{1}$ An anti-crossing of the dot and nanocavity resonances occurs as the temperature is increased from 15K to 29K. The zero-detuning splitting is 0.164 meV, slightly larger than the 0.13 meV coupled linewidth, so there is a dip between the peaks of 30-40{\%}. The 2D photonic crystal slab is surrounded by air; three holes in a line are omitted and the end holes are shifted out to form the cavity spacer.$^{2}$ The Q of the cavity mode was 13,300 at high power and about 6000 at the low power used for the anti-crossing. The volume of the cavity mode is computed to be about ($\lambda _{cav}$/n)$^{3}$ = 0.04 $\mu $m$^{3}$, where $\lambda _{cav}$ is the cavity mode wavelength and n is the refractive index. This solid-state system that entangles the quantum-dot-transition qubit with the cavity-mode-photon qubit may find applications in quantum information science as a deterministic single-photon source or quantum phase gate, or for quantum state transfer. 1. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature \textbf{432}, 200 (2004). 2. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, Nature \textbf{425}, 944 (2003).   

NMR-like Operation and Analysis of Decoherence of a Superconducting Quantum Bit

The Quantronium [1], a superconducting circuit with Josephson junctions, can be regarded as a solid state qubit prototype with built-in decoupling from its environment. We demonstrate that arbitrary operators can be applied to it using NMR-like and atomic physics-like techniques that involve quasi-resonant microwave or adiabatic DC pulses [2]. Then, we explain how the symmetry of the circuit limits decoherence of a superposition of states, at an optimal working point. Coherence time measurements, performed both during free and driven evolution of the qubit are presented and analyzed using a simple model involving different noise sources. A complete picture of decoherence in this quantum electrical circuit is thus provided. [1] D. Vion \textit{et al.}, Science \textbf{296} (2002). [2] E. Collin \textit{et al}., Phys. Rev. Lett. \textbf{93}, 15, (2004).   

Superconducting qubit storage and entanglement with nanomechanical resonators

I will discuss work done with Andrew N. Cleland on the design of a quantum computing architecture based on the integration of GHz-frequency mechanical or electromagnetic resonators with Josephson junction (JJ) phase qubits. This system is analogous to one or more few-level atoms (the JJs) in an electromagnetic cavity (the resonator), except that here we can individually tune the energy level spacing of each atom, and can control the electromagnetic interaction strength. We show that the quantum state of a JJ can be passed to the resonator and stored there, and later passed back to the original JJ or transferred to a second JJ. Furthermore, memory devices made from resonators with ultrahigh Q factors can used to effectively extend the coherence of the phase qubits. The resonator can also produce controlled entangled states of the JJs and can mediate quantum logic. We discuss the accuracy of the rotating-wave and adiabatic approximations in this system, and show that these approximations are actually quite poor at predicting the phase of probability amplitudes. Our architecture combines desirable features of both solid-state and cavity-QED approaches, and may make quantum computing possible in a scalable, solid-state environment.