Scattering of coherent states on a single artificial atom

In this work, we theoretically analyze a circuit quantum electrodynamics design where propagating quantum microwaves interact with a single artificial atom, a single Cooper-pair box. In particular, we derive a master equation in the so-called transmon regime, including coherent drives. Inspired by recent experiments, we then apply the master equation to describe the dynamics in both a two-level and a three-level approximation of the atom. In the two-level case, we also discuss how to measure photon antibunching in the reflected field and how it is affected by finite temperature and finite detection bandwidth.

[1]  T. Palomaki,et al.  Microwave quantum optics with an artificial atom in one-dimensional open space , 2012, 1210.4303.

[2]  A. Wallraff,et al.  Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system , 2008, Nature.

[3]  M. Devoret.  Quantum Fluctuations in Electrical Circuits , 1997 .

[4]  J J García-Ripoll,et al.  Microwave photon detector in circuit QED. , 2008, Physical review letters.

[5]  Shanhui Fan,et al.  Coherent photon transport from spontaneous emission in one-dimensional waveguides. , 2005, Optics letters.

[6]  Daniel J. Gauthier,et al.  Strongly correlated photons generated by coupling a three- or four-level system to a waveguide , 2012, 1202.2776.

[7]  P. Knight,et al.  Introductory quantum optics , 2004 .

[8]  Io-Chun Hoi,et al.  Generation of nonclassical microwave states using an artificial atom in 1D open space. , 2012, Physical review letters.

[9]  P. Zoller,et al.  Single-atom mirror for one-dimensional atomic lattice gases (20 pages) , 2006 .

[10]  L Frunzio,et al.  Generating single microwave photons in a circuit. , 2007, Nature.

[11]  Daniel J. Gauthier,et al.  Waveguide QED: Many-body bound-state effects in coherent and Fock-state scattering from a two-level system , 2010, 1009.5325.

[12]  M. Devoret,et al.  Quantum coherence with a single Cooper pair , 1998 .

[13]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.

[14]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[15]  Jens Koch,et al.  Coupling superconducting qubits via a cavity bus , 2007, Nature.

[16]  D. E. Chang,et al.  A single-photon transistor using nanoscale surface plasmons , 2007, 0706.4335.

[17]  Bernard Yurke,et al.  Quantum network theory , 1984 .

[18]  O. Astafiev,et al.  Resonance Fluorescence of a Single Artificial Atom , 2010, Science.

[19]  K. L. Hur.  Kondo resonance of a microwave photon , 2011, 1104.0708.

[20]  A. A. Abdumalikov,et al.  Dynamics of coherent and incoherent emission from an artificial atom in a 1D space. , 2011, Physical review letters.

[21]  D. Schuster,et al.  Measurement of the excited-state lifetime of a microelectronic circuit. , 2003, Physical review letters.

[22]  Büttiker.  Zero-current persistent potential drop across small-capacitance Josephson junctions. , 1987, Physical review. B, Condensed matter.

[23]  Y. Makhlin,et al.  Quantum-state engineering with Josephson-junction devices , 2000, cond-mat/0011269.

[24]  Io-Chun Hoi,et al.  Giant cross-Kerr effect for propagating microwaves induced by an artificial atom. , 2012, Physical review letters.

[25]  T. Duty,et al.  The single Cooper-pair box as a charge qubit , 2005 .

[26]  Y. Pashkin,et al.  Coherent control of macroscopic quantum states in a single-Cooper-pair box , 1999, Nature.

[27]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[28]  T. Duty,et al.  Coherent dynamics of a Josephson charge qubit , 2003, cond-mat/0305433.

[29]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[30]  T. Palomaki,et al.  Demonstration of a single-photon router in the microwave regime. , 2011, Physical review letters.

[31]  L Frunzio,et al.  ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field. , 2005, Physical review letters.

[32]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[33]  Alexander Shnirman,et al.  Cavity QED in superconducting circuits: susceptibility at elevated temperatures , 2004 .

[34]  G. Johansson,et al.  Readout methods and devices for Josephson-junction-based solid-state qubits , 2006, cond-mat/0602585.

[35]  A. A. Abdumalikov,et al.  Ultimate on-chip quantum amplifier. , 2010, Physical review letters.

[36]  S. Girvin,et al.  Wiring up quantum systems , 2008, Nature.

[37]  R. J. Schoelkopf,et al.  Resolving photon number states in a superconducting circuit , 2007, Nature.

[38]  J. Clarke,et al.  Superconducting quantum bits , 2008, Nature.

[39]  S. Fan,et al.  Resonance fluorescence in a waveguide geometry , 2011, 2012 Conference on Lasers and Electro-Optics (CLEO).

[40]  Shanhui Fan,et al.  Coherent single photon transport in one-dimensional waveguide coupledwith superconducting quantum bits , 2005, 2006 Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science Conference.

[41]  A. A. Abdumalikov,et al.  Electromagnetically induced transparency on a single artificial atom. , 2010, Physical review letters.