Latest Papers

Exploiting the intrinsic nonlinearity of superconducting Josephson junctions, we propose a scalable circuit with superconducting qubits (SCQs) which is very similar to the successful one now being used for trapped ions. The SCQs are coupled to the "vibrational" mode provided by a superconducting LC circuit or its equivalent (e.g., a SQUID). Both single-qubit rotations and qubit-LC-circuit couplings/decouplings can be controlled by the frequencies of the time-dependent magnetic fluxes. The circuit is scalable since the qubit-qubit interactions, mediated by the LC circuit, can be selectively performed, and the information transfer can be realized in a controllable way.

Circuit QED is a promising solid-state quantum computing architecture. It also has excellent potential as a platform for quantum control -- especially quantum feedback control -- experiments. However, the current scheme for measurement in circuit QED is low efficiency and has low signal-to-noise ratio for single shot measurements. The low quality of this measurement makes the implementation of feedback difficult, and here we propose two schemes for measurement in circuit QED architectures that can significantly improve signal-to-noise, and potentially achieve quantum limited measurement. Such measurements would enable the implementation of quantum feedback protocols and we illustrate this with a simple entanglement stabilization scheme.

The original Jaynes-Cummings model is described by a Hamiltonian which is exactly solvable. Here we extend this model by several types of interactions leading to a nonhermitian operator which doesn't satisfy the physical condition of space-time reflection symmetry (PT symmetry). However the new Hamiltonians are either exactly solvable admitting an entirely real spectrum or quasi exactly solvable with a real algebraic part of their spectrum.

We design theoretically a new device to realize the general quantum storage based on dcSQUID charge qubits. The distinct advantages of our scheme are analyzed in comparison with existing storage scenarios. More arrestingly, the controllable XY-model spin interaction has been realized for the first time in superconducting qubits, which may have more potential applications besides those in quantum information processing. The experimental feasibility is also elaborated.

The Jaynes-Cummings model is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight (S. J. D. Phoenix, P. L. Knight, Annals of Physics 186, 381). of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e. where the rate of change of the two are anti-correlated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anti-correlation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix.

A nondegenerate two-photon Jaynes-Cummings model is investigated where the leakage of photon through the cavity is taken into account. The effect of cavity damping on the mean photon number, atomic populations, field statistics and both field and atomic squeezing is considered on the basis of master equation in dressed-state approximation for initial coherent fields and excited atom.

In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 90 % can be attained. We perform a dispersive measurement of the qubit state by coupling the qubit non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. The qubit coherence time is determined to be larger than 500 ns in a measurement of Ramsey fringes.

It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for certain shape-invariant potentials, including a non-hermitian version of the standard Jaynes-Cummings model for which the parent supersymmetric Hamiltonian is the superoscillator. The positive-definite metric operator in the Hilbert space is constructed explicitly along with the introduction of a new inner product structure, so that the eigenstates form a complete set of orthonormal vectors and the time-evolution is unitary.

We present a new experimental protocol for performing universal gates in a register of superconducting qubits coupled by fixed on-chip linear reactances. The qubits have fixed, detuned Larmor frequencies and can remain, during the entire gate operation, biased at their optimal working point where decoherence due to fluctuations in control parameters is suppressed to first order. Two-qubit gates are performed by simultaneously irradiating two qubits at their respective Larmor frequencies with appropriate amplitude and phase, while one-qubit gates are performed by the usual single-qubit irradiation pulses.

In this paper we point out that the Jaynes-Cummings model without taking a renonance conditon gives a non-commutative version of the simple spin model (including the parameters $x$, $y$ and $z$) treated by M. V. Berry. This model is different from usual non-commutative ones because the x-y coordinates are quantized, while the z coordinate is not. One of new and interesting points in our non-commutative model is that the strings corresponding to Dirac ones in the Berry model exist only in states containing the ground state (${\cal F}\times \{\ket{0}\} \cup \{\ket{0}\}\times {\cal F}$), while for other excited states (${\cal F}\times {\cal F} \setminus {\cal F}\times \{\ket{0}\} \cup \{\ket{0}\}\times {\cal F}$) they don't exist. It is probable that a non-commutative model makes singular objects (singular points or singular lines or etc) in the corresponding classical model mild or removes them partly.

Many protocols for quantum computation require a quantum memory element to store qubits. We discuss the accuracy with which quantum states prepared in a Josephson junction qubit can be stored in a nanoelectromechanical resonator and then transfered back to the junction. We find that the fidelity of the memory operation depends on both the junction-resonator coupling strength and the location of the state on the Bloch sphere. Although we specifically focus on a large-area, current-biased Josesphson junction phase qubit coupled to the dilatational mode of a piezoelectric nanoelectromechanical disk resonator, many our results will apply to other qubit-oscillator models.

We describe the design for a scalable, solid-state quantum-information-processing architecture based on the integration of GHz-frequency nanomechanical resonators with Josephson tunnel junctions, which has the potential for demonstrating a variety of single- and multi-qubit operations critical to quantum computation. The computational qubits are eigenstates of large-area, current-biased Josephson junctions, manipulated and measured using strobed external circuitry. Two or more of these phase qubits are capacitively coupled to a high-quality-factor piezoelectric nanoelectromechanical disk resonator, which forms the backbone of our architecture, and which enables coherent coupling of the qubits. The integrated system is analogous to one or more few-level atoms (the Josephson junction qubits) in an electromagnetic cavity (the nanomechanical resonator). However, unlike existing approaches using atoms in electromagnetic cavities, here we can individually tune the level spacing of the ``atoms'' and control their ``electromagnetic'' interaction strength. We show theoretically that quantum states prepared in a Josephson junction can be passed to the nanomechanical resonator and stored there, and then can be passed back to the original junction or transferred to another with high fidelity. The resonator can also be used to produce maximally entangled Bell states between a pair of Josephson junctions. Many such junction-resonator complexes can assembled in a hub-and-spoke layout, resulting in a large-scale quantum circuit. Our proposed architecture combines desirable features of both solid-state and cavity quantum electrodynamics approaches, and could make quantum information processing possible in a scalable, solid-state environment.

We have spectroscopically measured the energy level separation of a superconducting charge qubit coupled non-resonantly to a single mode of the electromagnetic field of a superconducting on-chip resonator. The strong coupling leads to large shifts in the energy levels of both the qubit and the resonator in this circuit quantum electrodynamics system. The dispersive shift of the resonator frequency is used to non-destructively determine the qubit state and to map out the dependence of its energy levels on the bias parameters. The measurement induces an ac-Stark shift of 0.6 MHz per photon in the qubit level separation. Fluctuations in the photon number (shot noise) induce level fluctuations in the qubit leading to dephasing which is the characteristic back-action of the measurement. A cross-over from lorentzian to gaussian line shape with increasing measurement power is observed and theoretically explained. For weak measurement a long intrinsic dephasing time of T_2 > 200 ns of the qubit is found.

We show that the relaxation and decoherence rates 1/T_1 and 1/T_2 of a qubit coupled to several noise sources are in general not additive, i.e., that the total rates are not the sums of the rates due to each individual noise source. To demonstrate this, we calculate the relaxation and pure dephasing rates 1/T_1 and 1/T_φof a superconducting (SC) flux qubit in the Born-Markov approximation in the presence of several circuit impedances Z_i using network graph theory and determine their deviation from additivity (the mixing term). We find that there is no mixing term in 1/T_φand that the mixing terms in 1/T_1 and 1/T_2 can be positive or negative, leading to reduced or enhanced relaxation and decoherence times T_1 and T_2. The mixing term due to the circuit inductance L at the qubit transition frequency ω_{01} is generally of second order in ω_{01}L/Z_i, but of third order if all impedances Z_i are pure resistances. We calculate T_{1,2} for an example of a SC flux qubit coupled to two impedances.

Solid state qubits realized in superconducting circuits are potentially extremely scalable. However, strong decoherence may be transferred to the qubits by various elements of the circuits that couple individual qubits, particularly when coupling is implemented over long distances. We propose here an encoding that provides full protection against errors originating from these coupling elements, for a chain of superconducting qubits with a nearest neighbor anisotropic XY-interaction. The encoding is also seen to provide partial protection against errors deriving from general electronic noise.

We propose an approach to reconstruct any superconducting charge qubit state by using quantum state tomography. This procedure requires a series of measurements on a large enough number of identically prepared copies of the quantum system. The experimental feasibility of this procedure is explained and the time scales for different quantum operations are estimated according to experimentally accessible parameters. Based on the state tomography, we also investigate the possibility of the process tomography.

Under appropriate conditions, superconducting electronic circuits behave quantum mechanically, with properties that can be designed and controlled at will. We have realized an experiment in which a superconducting two-level system, playing the role of an artificial atom, is strongly coupled to a single photon stored in an on-chip cavity. We show that the atom-photon coupling in this circuit can be made strong enough for coherent effects to dominate over dissipation, even in a solid state environment. This new regime of matter light interaction in a circuit can be exploited for quantum information processing and quantum communication. It may also lead to new approaches for single photon generation and detection.

We present a mathematical procedure which leads us to obtain analytical solutions for the atomic inversion and Wigner function in the framework of the Jaynes-Cummings model with an external quantum field, for any kinds of cavity and driving fields. Such solutions are expressed in the integral form, with their integrands having a commom term that describes the product of the Glauber-Sudarshan quasiprobability distribution functions for each field, and a kernel responsible for the entanglement. Considering two specific initial states of the tripartite system, the formalism is then applied to calculate the atomic inversion and Wigner function where, in particular, we show how the detuning and amplitude of the driving field modify the entanglement. In addition, we also obtain the correct

Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three various variants of two-photon q-deformed Jaynes-Cummings model.With the the field initially being in three different types of q-deformed coherent states,the quantum collapse and revival effects as well as atomic diploe squeezing are studied for both on-and off-resonant atom-field interaction. Particularly, it is shown that for nonzero detuning the atomic inversion exhibits superstructures which are absent in the non-deformed Jaynes-Cummings model and the dipole squeezing may be enhanced.

In this paper the possibility of generating nonlinear coherent states of the radiation field in a micromaser is explored. It is shown that these states can be provided in a lossless micromaser cavity under the weak Jaynes-Cummings interaction with intensity-dependent coupling of large number of individually injected two-level atoms in a coherent superposition of the upper and lower states. In particular, we show that the so-called nonlinear squeezed vacuum and nonlinear squeezed first excited states, as well as the even and odd nonlinear coherent states can be generated in the presence of two-photon transitions.