Session H33: Focus Session: Superconducting Qubits I

A quantum trajectory approach to circuit QED

Circuit QED is a promising area of research as it opens the possibility to realize the extreme strong coupling limit of cavity QED using superconducting electrical circuits. In this regime, quantum effects become dominant and a full quantum treatment of the system is essential. In this talk, I will show how continuous-in-time measurement theory can be used to obtain a quantum trajectory description of the qubit evolution conditioned on the measurement output. This conditional quantum trajectory describes the quantum non-demolition measurements used by the Schoelkopf group at Yale. Using this approach, we investigate measurement-induced dephasing, the effect of relaxation on measurement fidelity and the extreme strong coupling limit where effects such as number splitting occur. This description also opens the door to the investigation of non-linearities present in the Yale expriment.   

Theoretical and Experimental Studies of Circuit QED Systems (Part I)

The formalism of circuit QED explains the coupling between a superconducting qubit (charge or flux) and a microwave resonator. Instead of focusing on the well-known resonant and dispersive regimes, we investigate a deeply dispersive regime, where qubit and resonator are strongly detuned and the transition frequency of the resonator is almost negligible compared to the qubit one. This regime has been exploited experimentally in several different implementations, e.g., the reading-out of a superconducting qubit by means of a low frequency resonator. In this framework, we have developed a simple formalism which encompasses the many explanations given in the literature on the experiments mentioned above. Furthermore, our results shed new light on decoherence studies of dephasing mechanisms due to low frequency noise as well as photon noise.   

Theoretical and Experimental Studies of Circuit QED Systems (Part II)

In recent years, the interaction between superconducting qubits and on-chip microwave resonators has been investigated in theory and in experiment. We performed microwave spectroscopy on a system composed of a superconducting flux qubit and the single mode of an LC circuit resonator. The latter is formed by the shunting capacitance and its associated line inductance of the dc SQUID used to read-out the qubit state. Our implementation provides a counterpart to experiments in which the state of the microwave field is detected. The data shows clear evidence of the coupled system (coupling constant: few tens of MHz). Simulations of a dissipationless driven Jaynes-Cummings-like model allow us to estimate the effective number of photons present in the resonator. One possible interesting application would be the generation of microwave single photons.   

Phase Purcell Effect and the Crossover to Strong Coupling in Dispersive Circuit QED

We study the decoherence of a superconducting qubit due to the dispersive coupling to a damped harmonic oscillator. We go beyond the weak qubit-oscillator coupling, which we associate with a {\it phase Purcell effect}, and enter into an unexplored decoherence regime, solving a theoretical inconsistency in existing models: the divergence of the qubit dephasing rate in the absence of environment. Our results can be applied, with small adaptations, to a large variety of other physical systems, e.g. trapped ions and cavity QED, boosting theoretical and experimental decoherence studies.   

Single microwave photon source using circuit QED

In circuit QED, a superconducting charge qubit is fabricated inside a high-quality factor transmission line resonator [1]. This opens the possibility to probe the regime of strong coupling of cavity QED using microwave photons and artificial atoms. This physics was experimentally investigated in the resonant [2] and in the dispersive [3] regime. In this talk, we will show how this setup could be used to generate single microwave photons on demand. Moreover, by using a different circuit QED layout with two resonators, photon generation could be tagged. The possibility to use a similar setup to detect single photons will also be discussed. [1] A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin and R. J. Schoelkopf, Phys. Rev. A \textbf{69}, 062320 (2004). [2] A. Wallraff, D. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin and R. J. Schoelkopf, Nature \textbf{431}, 162 (2004). [3] D. I. Schuster, A. A. Houck, J. A. Schreier, A. Wallraff, J. M. Gambetta, A. Blais, L. Frunzio, B. Johnson, M. H. Devoret, S. M. Girvin and R. J. Schoelkopf, Cond-mat/0608693.   

Dispersive single photon non-linear optics with circuit QED

Circuit quantum electrodynamics couples a superconducting qubit to a high quality factor microwave cavity[1]. The strong coupling limit is reached when the cavity is resonant with the qubit, and the interaction between them dominates over decoherence[2]. If in addition, when the qubit and cavity are far off resonance, the dispersive frequency shifts are still larger than the decay rates, then the strong dispersive limit will be reached. In this regime, the qubit absorption spectrum resolves into individual photon number peaks[3]. The dual of this photon numbersplitting is that the cavity inherits some of the non-linearity of the qubit. This inherited non-linearity can be used to create photonic qubits and create quantum states of light in the cavity. [1] Blais, et. al. PRA, 2004, 69, 062320 [2] Wallraff, et. al. Nature, 2004, 431, 162 [3] Schuster, et. al. Nature, 2006, in press   

Coupling two superconducting qubits via a cavity

In a recent experiment [1] we have demonstrated that a superconducting qubit can be coupled strongly to a transmission line cavity. The qubit is able to swap its state with the cavity. Presently we place two qubits in the cavity which both can exchange their state with the cavity. This exchange establishes a coupling between qubits placed at the opposite end of the cavity. We discuss possible realizations of two-qubit gates and provide preliminary experimental results. [1] A. Wallraff et al., Nature (London) 431, 162 (2004)   

Cavity QED with a Josephson Phase Qubit

A superconducting qubit coupled to a microwave resonator is a solid state implementation of cavity quantum electrodynamics. This system allows a study of the coherent interaction of a macroscopic two-level system with a single photon in the strong coupling limit. We have investigated a Josephson phase qubit capacitively coupled to a superconducting coplanar waveguide resonator (CPW). The phase qubit is tunable over a wide frequency range and can thus be brought in and out of resonance with the CPW. Vacuum Rabi oscillations and cavity quantization can be probed spectroscopically as well as in the time domain. An arbitrary quantum state can be initialized in the phase qubit and transferred to the CPW. Using the qubit as sensitive probe of the resonator the relaxation time T$_1$ as well as the dephasing time T$_2$ of the resonator can be measured directly. With lifetimes of the order of several microseconds, high Q resonators are envisioned to act as storage elements for the quantum state of a qubit or as inter-qubit communication bus.   

Probing Multiphoton Dressed States of a Superconducting Qubit

There has been great interest in the new field of circuit QED, where the interaction of photons and matter are studied in the context of superconducting qubits. In this work, we create dressed states of a superconducting qubit, the single Cooper-pair box (SCB), with an intense microwave ($\sim $7 GHz) drive. The dressed states represent the hybridization of the qubit and photon degrees of freedom, and appear as avoided level crossings (ALC) in the combined qubit-photon energy diagram. The ALC occur when the energy of n photons is resonant with the charging energy of the SCB. By embedding the circuit in an rf resonator ($\sim $650 MHz), we can directly probe the dressed states. When the dressed states are off resonance, we see a purely reactive response, analogous to the quantum capacitance. On resonance, we see that the dressed qubit absorbs energy from the resonator. For some conditions, we also see evidence of population inversion in the dressed states, indicated by amplification of the reflected rf field and a negative quantum capacitance. All these effects can be explained by including relaxation in the dressed state picture.   

2D cavity grid quantum computing

We propose a novel scheme for scalable solid state quantum computing, where superconducting microwave transmission line resonators (cavities) are arranged in a two-dimensional grid on the surface of a chip, coupling to superconducting qubits (charge or flux) at the intersections. We analyze how tasks of quantum information processing can be implemented in such a topology, including efficient two-qubit gates between any two qubits, initialization and read-out. The effects of decoherence, fabrication imperfections and inhomogeneities will be addressed.   

Quantum teleportation using circuit cavity-QED systems

We investigate the experimental prospects for a probabilistic quantum teleportation scheme. In particular, we consider a system composed of coupled superconducting Josephson-junction phase qubits and superconducting transmission line resonators. The relatively short lived phase qubits are used only to prepare states, mediate entanglement, and readout. The longer lived resonators play the traditional role of qubits, providing the entanglement channel and logical basis.   

Cavity QED and magnetic field modulated coupling between two-level resonators and a Josephson junction

A superconducting Josephson junction can be explored as a novel probe of the amorphous two-level systems (TLSs) inside the junction. In recent experiments, TLSs have been demonstrated in the energy splittings of the superconducting phase qubits. However, the mechanism of the coupling between the TLSs and the junction remains unresolved. Possible mechanisms include coupling of the TLSs with the critical current and coupling of the TLSs with the dielectric field in the junction. In this talk, we present a scheme that can distinguish the two mechanisms. The key idea is to apply a magnetic field inside the junction, which is treated as a high-Q cavity, and study the cavity transmission in the presence of the TLS. When the TLS couples with the critical current, the magnitude of the coupling will be strongly modulated by the magnetic field; when the TLS couples with the dielectric field, the magnitude of the coupling will not be affected. The change of the coupling can be observed through the cavity transmission. We calculate the cavity transmission under the magnetic field and show that the dependence of the coupling on the field can be extracted from the amplitude and the spectrum of the transmission. We also show that spatial location of the TLS can be resolved by this scheme.   

Coherent coupling between a Josephson phase qubit and an LC resonant cavity

We have taken the first step towards the implementation of cavity QED quantum information processing with Josephson phase qubits. We have observed for the first time a coherent interaction between a phase qubit and an LC cavity formed by a 7 mm long coplanar waveguide resonant at 9 GHz. At the co- resonant point of the qubit and cavity, we observe splitting of the qubit's spectral line. In a time-domain measurement, we observe coherent vacuum Rabi oscillations between the qubit and oscillator.