Session S15: Superconducting Qubits III

Transmission line cavity as a quantum memory for superconducting phase qubits

A superconducting transmission line cavity coupling two phase qubits has already proven useful as a bus for coherent state transfer$^1$. In this talk we will discuss our efforts in extending the work of Sillanpa\"{a} \textit{et al.}\footnote{NATURE 449, 438-442 (2007)} to use a transmission line as a short term memory element.   

Coplanar resonators as computational elements in a superconducting qubit architecture

We are coupling a superconducting phase qubit, implemented using a current-biased Josephson junction, to a high-Q coplanar waveguide resonator. The interaction between the phase qubit and the resonator can be controlled by tuning the qubit frequency into and out of resonance with the resonator, a tuning that can be achieved dynamically over times short compared to the Rabi time. By combining the quantum control flexibility of the phase qubit with the long coherence time and bosonic nature of the resonator, a number of interesting quantum operations can be explored, including long-term phase coherent quantum memory and two-qubit bus architectures. In this talk we will report on our recent progress with this experiment.   

Entangling phase qubits via a common transmission line cavity

We consider ways of ``distributing'' entanglement to a number of qubits via a common superconducting transmission line cavity. We propose methods of preparing such states and verifying its preparation.   

Measuring the quantum states of a superconducting cavity

We consider the prospects for preparing and measuring some basic quantum states (e.g. number states) of a superconducting transmission line cavity coupled to Josephson-junction qubits.   

Cooling of a Resonator with Microwave Induced Charge-Phase Qubit Transitions

We have studied a circuit QED experiment where a superconducting charge-phase qubit is coupled to an electric $rf$-resonator via the phase degree of freedom. The resonator is coupled to a transmission line that allows reflection measurement with narrow band detection. Additionally, the charge degree of freedom is coupled to a $\mu$w-signal. The level spacing $\hbar\Omega$ of the qubit is controlled with constant shifts in both degrees of freedom. Multiphoton absorption from both drives can excite the qubit in the case the level separation is equal to the sum of the photon energies. The results of the measurements show asymmetry between the depths of the side-resonances of the basic resonance $\Omega=\omega_{\mu w}$. Also, a non-monotonic AC-Stark shift is observed in the apparent resonance positions. Solutions of the semiclassical Maxwell-Bloch equations of the whole measurement apparatus show that the measured results can be considered as evidence of cooling/heating of the oscillator.   

Fast tuning of a high Q microwave cavity for qubit coupling.

In 2004 Wallraff {\it et al.}[1] demonstrated that an artificial atom in form of a superconducting qubit can exhibit coherent interaction with a superconducting high Q microwave transmissionline resonator. In recent experiments [2,3] similar resonators have been used for coupling and reading out qubits. In these experiments the resonance frequency of the resonator is fixed and the qubit frequency is tuned. Here we present measurements on a superconducting transmission line resonator with a tunable resonance frequency that could be used for qubit coupling [4]. With such a device, qubit gates can be performed while the qubits stay at their optimal points. We demonstrate a tunability of 700 MHz for a 4.8 GHz resonator with a linewidth of 500 kHz and that we can tune the resonance frequency by 330 MHz in a few ns. We show that if the resonator is detuned faster than its decay time the photons inside the resonator will shift their frequency with the resonator. \newline [1] A. Wallraff, {\it et al.}, Nature {\bf 431}, 162 (2004). \newline [2] J. Majer, {\it et al.}, Nature {\bf 449}, 443 (2007). \newline [3] M.A. Sillanp\"a, J.I. Park, and R.W. Simmonds, Nature {\bf 449}, 438 (2007). \newline [4] M. Wallquist, V.S. Shumeiko, and G. Wendin, Phys. Rev. B {\bf 74}, 224506 (2006).   

Vacuum Rabi Mode Splitting at High Drive Powers and Elevated Temperatures

The circuit QED architecture $[1,2]$ is ideal to probe the nonlinearity of a strongly coupled cavity QED system at high drive powers populating the cavity with a controllable average photon number in the range from 0.1 $<$ n $<$ 100. While in atomic cavity QED the radiation pressure exerted on the atoms by the drive tends to expel the atoms from the cavity, superconducting qubits remain at a fixed position and maintain constant coupling. This enables us to explore the cross-over from the quantum to the classical regime in the single qubit-field interaction by measuring vacuum Rabi mode splitting spectra. We also investigate the effect of thermal radiation in the cavity leading to a thermal population of excited states in the Jaynes-Cummings ladder, which was theoretically studied in Ref. $[3]$. Simulations have been carried out in order to determine the optimal set of qubit and resonator parameters needed for first experiments. \newline $[1]$ A. Blais \textit{et al.} Phys. Rev. A \textbf{69}, 062320 (2004). \newline $[2]$ A. Wallraff \textit{et al.} Nature \textbf{431}, 162 (2004). \newline $[3]$ I. Rau \textit{et al.} Phys. Rev. B \textbf{70}, 054521 (2004).   

Observation of Berry's Phase in a Superconducting Qubit

In quantum information science, the phase of a wavefunction plays an important role in encoding information. While most experiments in this field rely on dynamic effects to manipulate this information, an alternative approach is to use geometric phase, which has been argued to have potential fault tolerance [1]. Here we demonstrate the controlled accumulation of a geometric phase, Berry's phase, in a superconducting qubit, manipulating the qubit geometrically using microwave radiation, and observing the accumulated phase in an interference experiment [2]. This is achieved utilising the excellent phase coherence and qubit control possible in Circuit QED [3]. We find excellent agreement with Berry's predictions, and also observe a geometry dependent contribution to dephasing. \newline [1] J.A. Jones et al, Nature 403, 869 (2000) \newline [2] P.J. Leek et al, Science, 22 November 2007 (10.1126/science.1149858) \newline [3] A. Wallraff et al, Nature 431, 162 (2004)   

Cooper Pair Box Qubit in the Ultrastrong Coupling Regime

We propose a new superconducting qubit design, where a small Josephson junction is inserted in the central conductor of a coplanar waveguide resonator. In this distributed element design, the resonator provides a negative reactance for the junction, which modifies the charging energy $E_C$ of the junction and places the qubit far in the ``Transmon regime'', $E_J \gg E_C$, where $E_J$ is the Josephson energy of the junction. We will discuss design details and show preliminary fabrication and measurement results.   

Homodyne detection of resonance fluorescence in circuit QED

In circuit QED, the transmon qubit[1] allows long coherence times and strong coupling. In this regime, tuning the qubit into resonance with the cavity leads to vacuum Rabi splitting[2] with two transmission peaks very well-resolved in frequency ($\sim$300 linewidths apart). At low probe power, these peaks have Lorentzian shape. As the probe power is increased, each Rabi peak is observed to split into two peaks. Approximating the combined qubit and cavity as a two-level system and applying the theory of resonance fluorescence reproduces the main features of this phenomenon. We explore the effects of including additional levels of the transmon and cavity in the detailed theoretical modeling of the experiment. Additionally, we discuss the possibility to observe the Mollow triplet in the fluorescence spectrum. \newline[1] Jens Koch, TM Yu, JM Gambetta, AA Houck, DI Schuster, J Majer, A Blais, MH Devoret, SM Girvin, and RJ Schoelkopf. Phys. Rev. A \textbf{76}, 042319 (2007) \newline[2] A Wallraff, D Schuster, A Blais, L Frunzio, R-S Huang, J Majer, S Kumar, SM Girvin and RJ Schoelkopf, Nature \textbf{431}, 162 (2004)   

Purcell Effect Limits on the Lifetimes of Transmon Qubits

Circuit QED couples a superconducting qubit to a transmission line cavity. The presence of the cavity can suppress or enhance the spontaneous emission of the qubit into the cavity, a phenomenon known as the Purcell effect. Consequently, the qubit excited-state lifetime depends on the qubit-cavity detuning. A quantum mechanical calculation of the Purcell effect for a single mode of the cavity does not account for T1s observed in our system. Here we show a semi-classical approximation for the Purcell effect for a multi-mode cavity which we compare with T1 measurements of several transmon [1] qubits. By designing an appropriate cavity we have improved T1 by a factor of 10. \newline \newline[1] Charge-insensitive qubit design derived from the Cooper pair box. Jens Koch et al, Phys. Rev. A 76, 042319 (2007).   

Suppressing Charge Noise Decoherence in a Transmon Qubit

Here we discuss coherence measurements of the transmon qubit, an optimized Cooper Pair Box geometry. We show experimental verification that sensitivity to 1/f charge noise was exponentially suppressed in the transmon qubit. As a result, the effects of gate charge noise and quasiparticle poisoning have been nearly eliminated, and the qubit was seen to be nearly homogeneously broadened. Following an improvement in relaxation times, dephasing times were measured at over a microsecond, nearly twice the relaxation time, without the need of an echo experiment while being tuned over a range of several GHz. The tuning of the qubit excitation energy shows strong agreement with a quantum mechanical treatment of a two level system coupled to our read-out geometry; the spectrum is nearly devoid of unintended avoided crossings. The dephasing times measured are limited by relaxation and further improvements in relaxation time could be matched by dephasing time increases.   

Circuit QED with phase-biased qubits

Coupling of a superconducing charge qubit to a transmission line resonator has been shown to lead to the very strong coupling regime of cavity qubit [1]. ~In this talk, we will discuss an alternative approach to circuit QED based on the cavity bifurcation amplifier [2] and where a qubit is directly embedded in the resonator's center line. ~We will show that this type of phase bias leads to very strong coupling and/or non-linearities. ~Readout, decoherence rates and coupling of qubits in this architecture will be discussed. [1] A. Wallraff et al., Nature 431, 162 (2004). [2] M. Metcalfe et al., PRB 76, 174516 (2007).   

Quantum walk on a circle in phase space via superconducting circuit quantum electrodynamics

We show how a quantum walk, with a single walker and controllable decoherence, can be implemented for the first time in a quantum quincunx created via superconducting circuit quantum electrodynamics (QED). Two resonators are employed to provide simultaneously fast readout and controllable decoherence over a wide range of parameters. The Hadamard coin flip is achieved by directly driving the cavity, with the result that the walker jumps between circles in phase space but still exhibits quantum walk behavior over 15 steps.   

Quantum mirror transport of qudits and continuous variables and an implementation in Circuit-QED

We expand on our previous work [J. Fitzsimons and J. Twamley, Phys. Rev. Lett. 97, 090502 (2006)], to derive a globally controlled automata-like protocol for the perfect transmission of quantum information in a chain made up of qudits or a chain made up of harmonic oscillators. The resulting protocol results in perfect spatial reflection of the entire quantum state of the chain about its midpoint. Quantum information can be encoded and then processed in continuous variables if one can engineer highly squeezed states [S. Lloyd and S. L. Braunstein, Phys. Rev. Lett. 82, 1784 (1999)]. We show that appropriately driving a superconducting coplanar microwave cavity coupled to a Cooper-pair box qubit can generate very high squeezings of the cavity mode. We consider a linear array of coplanar cavities nearest-neighbor coupled by Cooper-pair boxes. By controlling the coupling strengths of the cavities to the coupling-CPB qubits and the decoherence rates of the latter with time, we show that we can initialize the cavities to be in highly squeezed CV states, and then execute globally controlled quantum mirroring of the entire chain of CV qubits. We finally show that with extra control on the end cavities of the chain we can further execute universal CV quantum computation.