Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits

The ability to generate particles from the quantum vacuum is one of the most pro- found consequences of Heisenberg's uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, may soon be able to realize the elusive verification of the dynamical Casimir effect and analogue Hawking radiation. This article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analogue, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.

[1]  Marco Lanzagorta,et al.  Quantum Simulators , 2013 .

[2]  Juha Hassel,et al.  Dynamical Casimir effect in a Josephson metamaterial , 2011, Proceedings of the National Academy of Sciences.

[3]  D. Dalvit.  Quantum physics: Shaking photons out of the vacuum , 2011, Nature.

[4]  S. Filipp,et al.  Observation of two-mode squeezing in the microwave frequency domain. , 2011, Physical review letters.

[5]  F. Nori,et al.  Atomic physics and quantum optics using superconducting circuits , 2011, Nature.

[6]  J. Fink,et al.  Experimental state tomography of itinerant single microwave photons. , 2011, Physical review letters.

[7]  A. Pourkabirian,et al.  Observation of the dynamical Casimir effect in a superconducting circuit , 2011, Nature.

[8]  Alexandre Blais,et al.  Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors , 2011 .

[9]  S. Filipp,et al.  Photon State Tomography for Two-Mode Correlated Itinerant Microwave Fields , 2011, 1101.2136.

[10]  E. Solano,et al.  Approaching perfect microwave photodetection in circuit QED , 2010, 1101.0016.

[11]  W. Unruh,et al.  Comment on "Hawking radiation from ultrashort laser pulse filaments". , 2010, Physical review letters.

[12]  S T Merkel,et al.  Microwave photon counter based on Josephson junctions. , 2010, Physical review letters.

[13]  L. Frunzio,et al.  Two-mode correlation of microwave quantum noise generated by parametric down-conversion. , 2010, Physical review letters.

[14]  Erik Lucero,et al.  Photon shell game in three-resonator circuit quantum electrodynamics , 2010, 1011.3080.

[15]  Erik Lucero,et al.  Deterministic entanglement of photons in two superconducting microwave resonators. , 2010, Physical review letters.

[16]  E. Solano,et al.  Circuit quantum electrodynamics in the ultrastrong-coupling regime , 2010 .

[17]  V. G. Sala,et al.  Hawking radiation from ultrashort laser pulse filaments. , 2010, Physical review letters.

[18]  F. Nori,et al.  Non-equilibrium Landauer Transport Model for Hawking radiation from a Black Hole , 2010 .

[19]  A. Houck,et al.  Dispersive photon blockade in a superconducting circuit. , 2010, Physical review letters.

[20]  G. Lawrence,et al.  Measurement of stimulated Hawking emission in an analogue system. , 2010, Physical review letters.

[21]  F. Nori,et al.  Dynamical Casimir effect in superconducting microwave circuits , 2010, 1007.1058.

[22]  T. Duty,et al.  Photon generation in an electromagnetic cavity with a time-dependent boundary. , 2010, Physical review letters.

[23]  E Solano,et al.  Observation of the Bloch-Siegert shift in a qubit-oscillator system in the ultrastrong coupling regime. , 2010, Physical review letters.

[24]  Jay M. Gambetta,et al.  Preparation and measurement of three-qubit entanglement in a superconducting circuit , 2010, Nature.

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

[26]  Canada,et al.  Schemes for the observation of photon correlation functions in circuit QED with linear detectors , 2010, 1004.3987.

[27]  P. D. Nation,et al.  The trilinear Hamiltonian: a zero-dimensional model of Hawking radiation from a quantized source , 2010, 1004.0522.

[28]  Erik Lucero,et al.  Quantum ground state and single-phonon control of a mechanical resonator , 2010, Nature.

[29]  U. Leonhardt.  Essential Quantum Optics: From Quantum Measurements to Black Holes , 2010 .

[30]  C. P. Sun,et al.  Single-photon switch: Controllable scattering of photons inside a one-dimensional resonator waveguide , 2010 .

[31]  M. Mariantoni,et al.  Planck spectroscopy and quantum noise of microwave beam splitters. , 2010, Physical review letters.

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

[33]  F. Nori,et al.  Natural and artificial atoms for quantum computation , 2010, 1002.1871.

[34]  M. Mariantoni,et al.  Dual-path state reconstruction scheme for propagating quantum microwaves and detector noise tomography. , 2010, Physical review letters.

[35]  F. Nori,et al.  Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states , 2009, 0912.4888.

[36]  R. J. Schoelkopf,et al.  Phase-preserving amplification near the quantum limit with a Josephson ring modulator , 2009, Nature.

[37]  J J García-Ripoll,et al.  Switchable ultrastrong coupling in circuit QED. , 2009, Physical review letters.

[38]  A. Lambrecht,et al.  Analogue Casimir radiation using an optical parametric oscillator , 2009, 0912.2853.

[39]  M. Devoret,et al.  Invited review article: The Josephson bifurcation amplifier. , 2009, The Review of scientific instruments.

[40]  F. Nori,et al.  Quantum Simulators , 2009, Science.

[41]  Erik Lucero,et al.  Decoherence dynamics of complex photon states in a superconducting circuit. , 2009, Physical review letters.

[42]  Cristiano Ciuti,et al.  Vacuum degeneracy of a circuit QED system in the ultrastrong coupling regime. , 2009, Physical review letters.

[43]  S. Mathur.  The information paradox: a pedagogical introduction , 2009, 0909.1038.

[44]  Franco Nori,et al.  Dynamical Casimir effect in a superconducting coplanar waveguide. , 2009, Physical review letters.

[45]  Cristiano Ciuti,et al.  Extracavity quantum vacuum radiation from a single qubit , 2009, 0906.2706.

[46]  Y. Kido,et al.  Dynamical Casimir effect for TE and TM modes in a resonant cavity bisected by a plasma sheet , 2009, 0906.2550.

[47]  Erik Lucero,et al.  Synthesizing arbitrary quantum states in a superconducting resonator , 2009, Nature.

[48]  M. Mariantoni,et al.  Quantum nondemolition photon detection in circuit QED and the quantum Zeno effect , 2009 .

[49]  J. Cirac,et al.  Hawking radiation from an acoustic black hole on an ion ring. , 2009, Physical review letters.

[50]  P. Nation,et al.  Analogue Hawking radiation in a dc-SQUID array transmission line. , 2009, Physical review letters.

[51]  G. Galeazzi,et al.  MIR: An experiment for the measurement of the dynamical Casimir effect , 2009 .

[52]  C. P. Sun,et al.  Controllable scattering of photons in a one-dimensional resonator waveguide , 2009 .

[53]  M. Visser.  Black holes in general relativity , 2009, 0901.4365.

[54]  P. Leek,et al.  Resolving Vacuum Fluctuations in an Electrical Circuit by Measuring the Lamb Shift , 2008, Science.

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

[56]  M. Blencowe,et al.  Intermodulation and parametric amplification in a superconducting stripline resonator integrated with a dc-SQUID , 2008, 0811.2571.

[57]  S. Girvin,et al.  Introduction to quantum noise, measurement, and amplification , 2008, 0810.4729.

[58]  Yasunobu Nakamura,et al.  Flux-driven Josephson parametric amplifier , 2008, 0808.1386.

[59]  Erik Lucero,et al.  Generation of Fock states in a superconducting quantum circuit , 2008, Nature.

[60]  G. C. Hilton,et al.  Amplification and squeezing of quantum noise with a tunable Josephson metamaterial , 2008, 0806.0659.

[61]  R. J. Schoelkopf,et al.  Analog information processing at the quantum limit with a Josephson ring modulator , 2008, 0805.3452.

[62]  T. Duty,et al.  Tuning the field in a microwave resonator faster than the photon lifetime , 2008 .

[63]  Franco Nori,et al.  Controllable scattering of a single photon inside a one-dimensional resonator waveguide. , 2008, Physical review letters.

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

[65]  P. Bertet,et al.  Tunable Resonators for Quantum Circuits , 2007, 0712.0221.

[66]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[67]  U. Leonhardt,et al.  Fiber-Optical Analog of the Event Horizon , 2007, Science.

[68]  Atsushi Higuchi,et al.  The Unruh effect and its applications , 2007, 0710.5373.

[69]  Mika A. Sillanpää,et al.  Coherent quantum state storage and transfer between two phase qubits via a resonant cavity , 2007, Nature.

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

[71]  Manuel Castellanos-Beltran,et al.  Widely tunable parametric amplifier based on a superconducting quantum interference device array resonator , 2007 .

[72]  F. Wilhelm,et al.  Dynamical tunneling in macroscopic systems. , 2007, Physical review letters.

[73]  A. Gossard,et al.  Frequency-selective single-photon detection using a double quantum dot. , 2007, Physical review letters.

[74]  S. Carlip.  Symmetries, horizons, and black hole entropy , 2007, 0705.3024.

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

[76]  E. Tholén,et al.  Nonlinearities and parametric amplification in superconducting coplanar waveguide resonators , 2007, cond-mat/0702280.

[77]  S. Lamoreaux.  Casimir forces: Still surprising after 60 years , 2007 .

[78]  G. Milburn,et al.  Linear optical quantum computing with photonic qubits , 2005, quant-ph/0512071.

[79]  S. Girvin,et al.  Resolving photon number states in a superconducting circuit , 2006, Nature.

[80]  B. Yurke,et al.  Prospects of employing superconducting stripline resonators for studying the dynamical Casimir effect experimentally , 2006, quant-ph/0606099.

[81]  M. Dykman.  Critical exponents in metastable decay via quantum activation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[82]  R. Onofrio,et al.  Detectability of dissipative motion in quantum vacuum via superradiance. , 2006, Physical review letters.

[83]  Carlos S. Frenk,et al.  The large-scale structure of the Universe , 2006, Nature.

[84]  Erik Lucero,et al.  Violation of Bell's inequality in Josephson phase qubits , 2009, Nature.

[85]  M. Dykman,et al.  Switching via quantum activation: A parametrically modulated oscillator (14 pages) , 2006, cond-mat/0602288.

[86]  F. Nori,et al.  Superconducting Circuits and Quantum Information , 2005, quant-ph/0601121.

[87]  F. Nori,et al.  Generation and control of Greenberger-Horne-Zeilinger entanglement in superconducting circuits. , 2005, Physical review letters.

[88]  V. Shumeiko,et al.  Superconducting Quantum Circuits, Qubits and Computing , 2005, cond-mat/0508729.

[89]  Michel Devoret,et al.  Superconducting quantum bits , 2005 .

[90]  A. Fabbri,et al.  Modeling Black Hole Evaporation , 2005 .

[91]  G. Galeazzi,et al.  A novel experimental approach for the detection of the dynamical Casimir effect , 2004, quant-ph/0411085.

[92]  R. Mann,et al.  Alice falls into a black hole: entanglement in noninertial frames. , 2004, Physical review letters.

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

[94]  W. Unruh,et al.  Hawking radiation in an electromagnetic waveguide? , 2004, Physical review letters.

[95]  R. Schutzhold,et al.  Universality of the Hawking effect , 2004, gr-qc/0408009.

[96]  P. Bertet,et al.  Coherent dynamics of a flux qubit coupled to a harmonic oscillator , 2004, Nature.

[97]  F. Nori,et al.  Generation of nonclassical photon states using a superconducting qubit in a microcavity , 2004, quant-ph/0402189.

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

[99]  D. Minic,et al.  What is Quantum Theory of Gravity , 2004, hep-th/0401028.

[100]  T.Padmanabhan.  Gravity and the Thermodynamics of Horizons , 2003, gr-qc/0311036.

[101]  T. Jacobson.  Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect , 2003, gr-qc/0308048.

[102]  Paul M. Alsing,et al.  Teleportation with a uniformly accelerated partner , 2003, SPIE International Symposium on Fluctuations and Noise.

[103]  Daniel R. Terno,et al.  Quantum Information and Relativity Theory , 2002, quant-ph/0212023.

[104]  J. Bekenstein.  Quantum Information and Quantum Black Holes , 2001, gr-qc/0107049.

[105]  M. Visser.  Essential and inessential features of Hawking radiation , 2001, hep-th/0106111.

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

[107]  Sergei P. Kulik,et al.  Quantum teleportation with a complete Bell state measurement , 2000, Physical review letters.

[108]  R. Parentani.  Quantum metric fluctuations and Hawking radiation , 2000, gr-qc/0009011.

[109]  J. Cirac,et al.  Sonic analog of gravitational black holes in bose-einstein condensates , 2000, Physical review letters.

[110]  D. Haviland,et al.  Superconducting and Insulating Behavior in One-Dimensional Josephson Junction Arrays , 2000, cond-mat/0001143.

[111]  R. Wald.  The Thermodynamics of Black Holes , 1999, Living reviews in relativity.

[112]  Weinfurter,et al.  Quantum cryptography with entangled photons , 1999, Physical review letters.

[113]  F. Wilczek,et al.  Hawking radiation As tunneling , 1999, Physical review letters.

[114]  Kouwenhoven,et al.  Double quantum dots as detectors of high-frequency quantum noise in mesoscopic conductors , 1999, Physical review letters.

[115]  R. Parentani.  Hawking radiation from Feynman diagrams , 1999, gr-qc/9904024.

[116]  V. Dodonov.  Dynamical Casimir effect in a nondegenerate cavity with losses and detuning , 1998 .

[117]  H. Weinfurter,et al.  Violation of Bell's Inequality under Strict Einstein Locality Conditions , 1998, quant-ph/9810080.

[118]  Kimble,et al.  Unconditional quantum teleportation , 1998, Science.

[119]  E. Chow,et al.  Length-Scale Dependence of the Superconductor-to-Insulator Quantum Phase Transition in One Dimension , 1998 .

[120]  T. Jacobson,et al.  Event horizons and ergoregions in 3He , 1998, cond-mat/9801308.

[121]  H. Weinfurter,et al.  Experimental quantum teleportation , 1997, Nature.

[122]  Dag Hanstorp,et al.  Fine structure of As− , 1997 .

[123]  D. Dalvit,et al.  Renormalization Group Approach to the Dynamical Casimir Effect , 1997, quant-ph/9710048.

[124]  R. Schutzhold,et al.  TREMBLING CAVITIES IN THE CANONICAL APPROACH , 1997, quant-ph/9709008.

[125]  Jongwoong Park,et al.  Production of photons by the parametric resonance in the dynamical Casimir effect , 1997, quant-ph/9706007.

[126]  S. Schiller,et al.  Measurement of the quantum states of squeezed light , 1997, Nature.

[127]  L. Ford,et al.  Cosmological and black hole horizon fluctuations , 1997, gr-qc/9704050.

[128]  S. Lamoreaux.  DEMONSTRATION OF THE CASIMIR FORCE IN THE 0.6 TO 6 MU M RANGE , 1997 .

[129]  Neto,et al.  Quantum radiation generated by a moving mirror in free space. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[130]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[131]  Reynaud,et al.  Motion Induced Radiation from a Vibrating Cavity. , 1996, Physical review letters.

[132]  Klimov,et al.  Generation and detection of photons in a cavity with a resonantly oscillating boundary. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[133]  Gignoux,et al.  Exponential growth of the energy of a wave in a 1D vibrating cavity: Application to the quantum vacuum. , 1996, Physical review letters.

[134]  Schieve,et al.  Radiation modes of a cavity with a moving boundary. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[135]  V. Dodonov.  Photon creation and excitation of a detector in a cavity with a resonantly vibrating wall , 1995 .

[136]  Sarkar,et al.  Moving mirrors and time-varying dielectrics. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[137]  Laflamme,et al.  Decoherence and recoherence in an analogue of the black hole information paradox. , 1994, Physical review. D, Particles and fields.

[138]  L. Ck.  Resonance response of the quantum vacuum to an oscillating boundary. , 1994 .

[139]  Hartle.  Spacetime information. , 1994, Physical review. D, Particles and fields.

[140]  Peter W. Milonni,et al.  The Quantum Vacuum: An Introduction to Quantum Electrodynamics , 1993 .

[141]  D. Nikonov,et al.  Quantum phenomena in resonators with moving walls , 1993 .

[142]  Beck,et al.  Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum. , 1993, Physical review letters.

[143]  Jacobson,et al.  Black-hole evaporation and ultrashort distances. , 1991, Physical review. D, Particles and fields.

[144]  L. Mandel,et al.  Induced coherence and indistinguishability in optical interference. , 1991, Physical review letters.

[145]  Barnett,et al.  Information theory, squeezing, and quantum correlations. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[146]  A. Kashlinsky,et al.  Large-scale structure in the Universe , 1991, Nature.

[147]  A. Klimov,et al.  Generation of squeezed states in a resonator with a moving wall , 1990 .

[148]  Smith,et al.  Observation of zero-point noise squeezing via a Josephson-parametric amplifier. , 1990, Physical review letters.

[149]  W. Case,et al.  The pumping of a swing from the seated position , 1990 .

[150]  Barnett,et al.  Entropy as a measure of quantum optical correlation. , 1989, Physical review. A, General physics.

[151]  E. Yablonovitch,et al.  Accelerating reference frame for electromagnetic waves in a rapidly growing plasma: Unruh-Davies-Fulling-DeWitt radiation and the nonadiabatic Casimir effect. , 1989, Physical review letters.

[152]  Rupp,et al.  Observation of parametric amplification and deamplification in a Josephson parametric amplifier. , 1989, Physical review. A, General physics.

[153]  Reid,et al.  Quantum correlations of phase in nondegenerate parametric oscillation. , 1988, Physical review letters.

[154]  Bernard Yurke,et al.  Observation of 4.2-K equilibrium-noise squeezing via a Josephson-parametric amplifier. , 1988, Physical review letters.

[155]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[156]  Yurke,et al.  Obtainment of thermal noise from a pure quantum state. , 1987, Physical review. A, General physics.

[157]  K. Likharev,et al.  Dynamics of Josephson Junctions and Circuits , 1986 .

[158]  Mertz,et al.  Observation of squeezed states generated by four-wave mixing in an optical cavity. , 1985, Physical review letters.

[159]  S. Barnett,et al.  Thermofield analysis of squeezing and statistical mixtures in quantum optics , 1985 .

[160]  C. Caves.  Quantum limits on noise in linear amplifiers , 1982 .

[161]  A. Barone,et al.  Physics and Applications of the Josephson Effect , 1982 .

[162]  N. D. Birrell,et al.  Quantum Fields in Curved Space: Curved spacetime examples , 1982 .

[163]  W. Unruh.  Experimental black hole evaporation , 1981 .

[164]  J. R. Letaw,et al.  Quantized scalar field in rotating coordinates , 1980 .

[165]  T. Claeson,et al.  Parametric amplification in arrays of Josephson tunnel junctions , 1977 .

[166]  W. Unruh.  Notes on black-hole evaporation , 1976 .

[167]  Stephen W. Hawking,et al.  Path Integral Derivation of Black Hole Radiance , 1976 .

[168]  David G. Boulware,et al.  Hawking radiation and thin shells , 1976 .

[169]  P. Davies,et al.  Radiation from a moving mirror in two dimensional space-time: conformal anomaly , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[170]  D. Page.  Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole , 1976 .

[171]  A. Ashtekar,et al.  Quantum fields in curved space-times , 1975, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[172]  D. Boulware.  Quantum Field Theory in Schwarzschild and Rindler Spaces , 1975 .

[173]  S. Hawking,et al.  Black hole explosions? , 1974, Nature.

[174]  Brandon Carter,et al.  The four laws of black hole mechanics , 1973 .

[175]  G. Moore.  Quantum Theory of the Electromagnetic Field in a Variable-Length One-Dimensional Cavity , 1970 .

[176]  B. Dewitt.  Quantum Theory of Gravity. I. The Canonical Theory , 1967 .

[177]  C. C. Wang,et al.  Nonlinear optics. , 1966, Applied optics.

[178]  R. H. Brown,et al.  Correlation between Photons in two Coherent Beams of Light , 1956, Nature.

[179]  Julian Schwinger,et al.  On gauge invariance and vacuum polarization , 1951 .

[180]  Willis E. Lamb,et al.  Fine Structure of the Hydrogen Atom by a Microwave Method , 1947 .

[181]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[182]  D. Roberts,et al.  On the attraction between two perfectly conducting plates , 2011 .

[183]  M. Devoret,et al.  The Josephson bifurcation amplifier , 2009 .

[184]  Adrian J Mulholland,et al.  Handbook of Theoretical and Computational Nanotechnology, Vol 6: Bioinformatics, Nanomedicine and Drug Design, Chapter 7 , 2006 .

[185]  P. Bergmann,et al.  Advances in the interplay between quantum and gravity physics , 2002 .

[186]  M. Evans.  Modern Nonlinear Optics Part I , 2001 .

[187]  B. Hu,et al.  Quantum fields in curved spacetime , 1997 .

[188]  Law.  Resonance response of the quantum vacuum to an oscillating boundary. , 1994, Physical review letters.

[189]  Myron W. Evans,et al.  Modern nonlinear optics , 1993 .

[190]  Steven Weinberg,et al.  The Cosmological Constant Problem , 1989 .

[191]  I. D. Karachentsev,et al.  Largescale Structure of the Universe , 1987 .

[192]  S. Christensen.  Quantum Theory of Gravity , 1984 .

[193]  S. Hawking.  Particle creation by black holes , 1975 .

[194]  P. Painlevé,et al.  Le Mecanique Classique et la Theorie de la Relativite. , 1921 .