Reading out the state inductively and microwave spectroscopy of an interferometer-type charge qubit

Born, D.; Шнырков, В. И.; Krech, W.; Wagner, Th.; Il’ichev, É. A.; Grajcar, M.; Hübner, Uwe; Meyer, H.‐G.

doi:10.1103/physrevb.70.180501

Cited by 41 publications

(37 citation statements)

References 14 publications

(18 reference statements)

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“…In particular in a closely related experiment, the level separation of a split Cooper pair box coupled inductively to a low frequency, moderate Q tank circuit has been determined spectroscopically [15]. The width and the saturation level of the spectroscopic lines discussed above depend sensitively on the power P s of the spectroscopic drive.…”

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confidence: 99%

ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field

et al. 2005

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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 T2 > 200 ns of the qubit is found.We have recently demonstrated that a superconducting quantum two-level system can be strongly coupled to a single microwave photon [1]. The strong coupling between a quantum solid state circuit and an individual photon, analogous to atomic cavity quantum electrodynamics (CQED) [2], has previously been envisaged by many authors, see Ref. 3 and references therein. Our circuit quantum electrodynamics architecture [3], in which a superconducting charge qubit, the Cooper pair box [4], is coupled strongly to a coplanar transmission line resonator, has great prospects both for performing quantum optics experiments [5] in solids and for realizing elements for quantum information processing [6] with superconducting circuits [7].In this letter we present spectroscopic measurements which demonstrate the non-resonant (dispersive) strong coupling between a Cooper pair box and a coherent microwave field in a high quality cavity. The quantum state of the Cooper pair box is controlled using resonant microwave radiation and is read out with a dispersive quantum non-demolition (QND) measurement [3,8,9]. The interaction between the Cooper pair box and the measurement field containing n photons on average gives rise to a large ac-Stark shift of the qubit energy levels, analogous to the one observed in CQED [10]. As a consequence of the strong coupling, quantum fluctuations in n induce a broadening of the transition line width, characterizing the back action of the measurement on the qubit.In our circuit QED architecture [3], see Fig. 1a, a split Cooper pair box [4], modelled by the two-level hamiltonian H a = −1/2 (E el σ x + E J σ z ) [11], is coupled capacitively to the electromagnetic field of a full wave (l = λ) transmission line resonator, described by a harmonic oscillator hamiltonian H r =hω r (a † a + 1/2). In the Cooper pair box, the energy difference E a =hω a = E 2 el + E 2 J between the ground state |↓ and the first excited state |↑ , see Fig. 1b, is determined by its electrostatic energy E el = 4E C (1 − n g ) and its Josephson ...

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confidence: 99%

ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field

et al. 2005

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“…Equation (18) for the voltage V coincides with the nonlinear equation (1) for the variable x with obvious change of the notations.…”

Section: Inductive Coupling With Lcr Resonator Parametric Inductancementioning

confidence: 99%

“…For characterization and controlling the states of superconducting qubits the one-photon spectroscopy was done by using relatively weak driving [11][12][13][14][15][16][17][18]. Matching of the ground and higher states with the one-photon energy was exploited to probe the upper levels of the Josephson-junction circuits [19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Multiphoton transitions in Josephson-junction qubits (Review Article)

Shevchenko¹,

Omelyanchouk²,

Il’ichev³

2012

Low Temperature Physics

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Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator's state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices.We present recent results for the driven superconducting qubit -resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau-Zener-Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing. Contents

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“…reflecting vortex states with a high degree of superconducting phase coherence, the deep minimum at f = 1/2 points to a state in which the phase coherence is strongly suppressed. More recently, it was realized that JJAs can be also used as quantum channels to transfer quantum information between distant sites (Ioffe et al 2002, Born et al 2004, Zorin 2004 Many authors have used a parallelism between the magnetic properties of 2D-JJA and granular high-temperature superconductors (HTS) to study some controversial features of HTS. It has been shown that granular superconductors can be considered as a collection of superconducting grains embedded in a weakly superconducting -or even normal -matrix.…”

Section: Introductionmentioning

confidence: 99%

Dynamical reentrance and geometry imposed quantization effects in Nb–AlO_x–Nb Josephson junction arrays

Araújo‐Moreira¹,

Sergeenkov²

2008

Supercond. Sci. Technol.

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Abstract. In this review, we report on different phenomena related to the magnetic properties of artificially prepared highly ordered (periodic) two-dimensional Josephson junction arrays (2D-JJA) of both shunted and unshunted Nb-AlO x -Nb tunnel junctions. By employing mutual-inductance measurements and using a high-sensitive home-made bridge, we have thoroughly investigated (both experimentally and theoretically) the temperature and magnetic field dependence of complex AC susceptibility of 2D-JJA. After brief description of the measurements technique and numerical simulations method, we proceed to demonstrate that the observed dynamic reentrance (DR) phenomenon is directly linked to the value of the Stewart-McCumber parameter β C . By simultaneously varying the inductance related parameter β L , we obtain a phase diagram β C -β L (which demarcates the border between the reentrant and non-reentrant behavior) and show that only arrays with sufficiently large value of β C will exhibit the DR behavior. The second topic of this review is related to the step-like structure (with the number of steps n = 4 corresponding to the number of flux quanta that can be screened by the maximum critical current of the junctions) which has been observed in the temperature dependence of AC susceptibility in our unshunted 2D-JJA with β L (4.2K) = 30 and attributed to the geometric properties of the array. The steps are predicted to manifest themselves in arrays with β L (T) matching a "quantization" condition β L (0)=2π(n+1).In conclusion, we demonstrate the use of the scanning SQUID microscope for imaging the local flux distribution within our unshunted arrays.

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Reading out the state inductively and microwave spectroscopy of an interferometer-type charge qubit

Cited by 41 publications

References 14 publications

ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field

ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field

Multiphoton transitions in Josephson-junction qubits (Review Article)

Dynamical reentrance and geometry imposed quantization effects in Nb–AlO_x–Nb Josephson junction arrays

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Reading out the state inductively and microwave spectroscopy of an interferometer-type charge qubit

Cited by 41 publications

References 14 publications

ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field

ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field

Multiphoton transitions in Josephson-junction qubits (Review Article)

Dynamical reentrance and geometry imposed quantization effects in Nb–AlOx–Nb Josephson junction arrays

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Dynamical reentrance and geometry imposed quantization effects in Nb–AlO_x–Nb Josephson junction arrays