Session A29: Focus Session: Quantum Optics with Superconducting Circuits: Hybrid Systems and Other Quantum Optics

Atomic physics and quantum optics using superconducting circuits: from the Dynamical Casimir effect to Majorana fermions

This talk will present an overview of some of our recent results on atomic physics and quantum optics using superconducting circuits. Particular emphasis will be given to photons interacting with qubits, interferometry, the Dynamical Casimir effect, and also studying Majorana fermions using superconducting circuits.\\[4pt] References available online at our web site:\\[0pt] J.Q. You, Z.D. Wang, W. Zhang, F. Nori, \textit{Manipulating and probing Majorana fermions using superconducting circuits,} (2011). Arxiv. J.R. Johansson, G. Johansson, C.M. Wilson, F. Nori, \textit{Dynamical Casimir effect in a superconducting coplanar waveguide,} Phys. Rev. Lett. \textbf{103}, 147003 (2009). \\[0pt] J.R. Johansson, G. Johansson, C.M. Wilson, F. Nori, \textit{Dynamical Casimir effect in superconducting microwave circuits,} Phys. Rev. A \textbf{82}, 052509 (2010). \\[0pt] C.M. Wilson, G. Johansson, A. Pourkabirian, J.R. Johansson, T. Duty, F. Nori, P. Delsing, \textit{Observation of the Dynamical Casimir Effect in a superconducting circuit. }Nature, in press (Nov. 2011). P.D. Nation, J.R. Johansson, M.P. Blencowe, F. Nori, \textit{Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits,} Rev. Mod. Phys., in press (2011). \\[0pt] J.Q. You, F. Nori, \textit{Atomic physics and quantum optics using superconducting circuits,} Nature \textbf{474}, 589 (2011). \\[0pt] S.N. Shevchenko, S. Ashhab, F. Nori, \textit{Landau-Zener-Stuckelberg interferometry,} Phys. Reports \textbf{492}, 1 (2010). \\[0pt] I. Buluta, S. Ashhab, F. Nori. \textit{Natural and artificial atoms for quantum computation, } Reports on Progress in Physics \textbf{74}, 104401 (2011). \\[0pt] I.Buluta, F. Nori, \textit{Quantum Simulators, }Science \textbf{326}, 108 (2009). \\[0pt] L.F. Wei, K. Maruyama, X.B. Wang, J.Q. You, F. Nori, \textit{Testing quantum contextuality with macroscopic superconducting circuits, } Phys. Rev. B \textbf{81}, 174513 (2010). \\[0pt] J.Q. You, X.-F. Shi, X. Hu, F. Nori, \textit{Quantum emulation of a spin system with topologically protected ground states using superconducting quantum circuit, } Phys. Rev. A \textbf{81}, 063823 (2010).   

Wigner Tomography of Classical and Non-Classical States in a Superconducting Anharmonic Oscillator

The Wigner quasi-probability distribution is a powerful tool for characterizing a quantum state and understanding the state dynamics in oscillators. Until now, there have been numerous measurements of this function in harmonic oscillators, and in particular in superconducting devices. However no similar measurement on anharmonic systems has been reported. We utilize the wide-range energy tunability in the multi-level Josephson phase qubit, biased in the small anharmonicity regime, to directly measure the Wigner function of various states. We measure non-classical superpositions of Fock-type states, as well as coherent-like states in this anharmonic system. This method provides an alternative to standard state tomography techniques which usually involve a long calibration process and have limited scalability for multi-level states.   

Geometric Phases, Noise and Non-adiabatic Effects in Multi-level Superconducting Systems

Geometric phases depend neither on time nor on energy, but only on the trajectory of the quantum system in state space. In previous studies [1], we have observed them in a Cooper pair box qubit, a system with large anharmonicity. We now make use of a superconducting transmon-type qubit with low anharmonicity to study geometric phases in a multi-level system. We measure the contribution of the second excited state to the geometric phase and find very good agreement with theory treating higher levels perturbatively. Furthermore, we quantify non-adiabatic corrections by decreasing the manipulation time in order to optimize our geometric gate. Geometric phases have also been shown to be resilient against adiabatic field fluctuations [2]. Here, we analyze the effect of artificially added noise on the geometric phase for different system trajectories. \newline [1] P.~J.~Leek \emph{et al.}, \emph{Science} \textbf{318}, 1889 (2007) \newline [2] S.~Filipp \emph{et al.}, \emph{Phys.~Rev.~Lett.~}\textbf{102}, 030404 (2009)   

Observing the geometric phase of a superconducting harmonic oscillator

Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase [1]. However, the linearity of the system precludes its observation without a non-linear quantum probe. We therefore make use of a superconducting qubit serving as an interferometer to measure the adiabatic geometric phase of a harmonic oscillator realized as an on-chip resonant circuit [2]. We study the geometric phase for a variety of trajectories and show that, in agreement with theory, it is proportional to the area enclosed by the trajectory in the space of coherent states. At the transition to the non-adiabatic regime, oscillatory dephasing effects caused by residual qubit-resonator entanglement are observed and analyzed. We also discuss the possibility of using the harmonic oscillator geometric phase to implement two-qubit phase gates. \\[4pt] [1] S.~Chaturvedi, M.~S.~Sriram, V.~Srinivasan, J.~Phys.~A: Math.~Gen.~{\bf 20}, L1071 (1987).\newline [2] M.~Pechal {\em et al.}, arXiv:1109.1157v1 [quant-ph].   

All-resonant control of superconducting resonator qudits

Quantum information processing with using superpositions of Fock states in superconducting resonators holds great promise for multi-level (i.e. qudit) quantum logic. Previous theoretical work has shown that a combination of dispersive and resonant interactions allow for general qudit logic operations. Here I introduce an all-resonant approach to control resonator qudits. This scheme allows for faster logic operations and will be compared to previous methods for Fock state generation and entangled state synthesis.   

Readout of Spin Systems with Superconducting Circuits

We present progress in coupling superconducting circuitry, in particular linear resonators and dispersive magnetometers, to an ensemble of spins. Species with a zero-field splitting (ZFS), such as bismuth doped silicon or NV centers in diamond, are particularly attractive as the absence of a strong magnetic bias field facilitates compatibility with superconducting devices. We present studies of the spin linewidth, and progress towards the observation of collective strong coupling. Furthermore, we will present data on the operation of a highly sensitive nanobridge SQUID magnetometer with a flux sensitivity of 26 $n\Phi_0/\sqrt{Hz}$ and tens of MHz of signal bandwidth. We also discuss the resilience of our superconducting measurement circuitry to in-plane magnetic fields, which can be used to tune the spin splitting.   

Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble

We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy (NV) centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus [1,2]. Using this circuit, we prepare arbitrary superpositions of the qubit states that we store into collective excitations of the spin ensemble and retrieve back later on into the qubit [3]. These results constitute a first proof of concept of spin-ensemble based quantum memory for superconducting qubits.\\[4pt] [1] Y. Kubo \textit{et al.}, Phys. Rev. Lett. \textbf{105}, 140502 (2010).\\[0pt] [2] Y. Kubo \textit{et al.}, arXiv: 1109.3960.\\[0pt] [3] Y. Kubo \textit{et al.}, arXiv: 1110.2978.   

Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond

We have experimentally demonstrated coherent strong coupling between a single macroscopic superconducting artificial atom (a gap tunable flux qubit [1]) and an ensemble of electron spins in the form of nitrogen--vacancy color centres in diamond. We have observed coherent exchange of a single quantum of energy between a flux qubit and a macroscopic ensemble consisting of about 3.0*10$^{7}$ NV- centers [2]. This is the first step towards the realization of a long-lived quantum memory and hybrid devices coupling microwave and optical systems. [1] \textit{Coherent operation of a gap-tunable flux qubit} X. B. Zhu, A. Kemp, S. Saito, K. Semba, APPLIED PHYSICS LETTERS, Volume: 97, Issue: 10 pp. 102503 (2010) [2] \textit{Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond} Xiaobo Zhu, Shiro Saito, Alexander Kemp, Kosuke Kakuyanagi, Shin-ichi Karimoto, Hayato Nakano, William J. Munro, Yasuhiro Tokura, Mark S. Everitt, Kae Nemoto, Makoto Kasu, Norikazu Mizuochi, and Kouichi Semba, Nature, Volume: 478, 221-224 (2011)   

Hybrid qubit-resonator systems: From strong to ultrastrong coupling, from equilibrium to non equilibrium phases

Hybrid systems : spin ensembles coupled to superconducting circuits have received a lot of attention recently. In a seminal experiment it has been demonstrated strong coupling between a NV-center spins ensemble and a flux qubit. The ensemble maps to a bosonic mode, thus this setup is a realization of a qubit-resonator model. In this talk we propose molecular magnets, instead of NV centers, as ensembles and we show that with them it is possible to reach the ultra strong coupling (the coupling is around $ 40 \% $ of the qubit-resonator frequencies). Finally, we emphasize the potentiality of these architectures for exploring many body physics by building arrays made of flux qubits and crystal spins. We will discuss non equilibrium signatures of Mott insulator - Superfluid phases and its feasibility within current technology.   

Quantum transducer in circuit optomechanics

Mechanical resonators are becoming macroscopic quantum objects with great potential. It is however difficult to measure and manipulate the phonon state due to the tiny motion in the quantum regime. We show that a superconducting microwave resonator linearly coupled to the mechanical mode constitutes a powerful probe and an interesting quantum source. This coupling is rendered much stronger than the usual radiation pressure interaction by adjusting a gate voltage and gives rise to coherent oscillations between phonons and photons. The phenomenon of phonon blockade is detected from the statistics of the light field [1] and a quantum tomography of the mechanical resonator is obtained after transferring the state to the microwave cavity. Quantum phonon states can also be synthesized from the cavity and hybrid entanglement can be engineered between phonons and photons. Mechanical resonators can furthermore be coupled to a large variety of quantum systems such as spins, optical photons, cold atoms, and Bose Einstein condensates. They act as a quantum transducer between an auxiliary quantum system and a microwave resonator, which is used as a quantum bus. The quantum communications are controlled with the individual gate voltages.\\[0pt] [1] N. Didier et al., Phys. Rev. B 84, 054503 (2011).