DOCSLIB.ORG

Quantum Optics with Electrical Circuits: Strong Coupling Cavity QED

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Optics with Electrical Circuits: Strong Coupling Cavity QED Quantum Optics with Electrical Circuits: Strong Coupling Cavity QED Ren-Shou Huang, Alexandre Blais, Andreas Wallraff, David Schuster, Sameer Kumar, Luigi Frunzio, Hannes Majer, Steven Girvin, Robert Schoelkopf Yale University ‘Circuit QED’ Blais et al. Phys. Rev. A 69, 062320 (2004) Wallraff et al. [cond-mat/0407325] Nature (in press) 2 Atoms Coupled to Photons 2s 2p Irreversible spontaneous decay into the photon continuum: 2 ps→+1 γ T1 ∼ 1 ns 1s Vacuum Fluctuations: (Virtual photon emission and reabsorption) Lamb shift lifts 1s 2p degeneracy Cavity QED: What happens if we trap the photons as discrete modes inside a cavity? 3 Outline Cavity QED in the AMO Community Optical Microwave Circuit QED: atoms with wires attached What is the cavity? What is the ‘atom’? Practical advantages Recent Experimental Results Quantum optics with an electrical circuit Future Directions 4 Cavity Quantum Electrodynamics (cQED) 2g = vacuum Rabi freq. κ = cavity decay rate γ = “transverse” decay rate t = transit time Strong Coupling = g > κ , γ , 1/t Jaynes-Cummings Hamiltonian E E Hˆ =+ω (aa††+ 1 ) el σσˆˆ− J −g(aσ−++σa) r 2 2 xz2 Electric dipole Quantized Field 2-level system Interaction 5 Cavity QED: Resonant Case ω = ω r 01 with interaction eigenstates are: 1 +=,0 ( ↑,1 +↓,0 ) 2 1 −=,0 ()↑,1 −↓,0 2 vacuum Rabi oscillations “dressed state ladders” 6 Microwave cQED with Rydberg Atoms vacuum Rabi oscillations beam of atoms; prepare in |e> 3-d super- conducting observe dependence of atom final cavity (50 GHz) state on time spent in cavity measure atomic state, or … Review: S. Haroche et al., Rev. Mod. Phys. 73 565 (2001) 7 cQED at Optical Frequencies State of photons is detected, not atoms. … measure changes in transmission of optical cavity 8 (Caltech group H. J. Kimble, H. Mabuchi) A Circuit Analog for Cavity QED 2g = vacuum Rabi freq. κ = cavity decay rate γ = “transverse” decay rate out cm 2.5 transmission λ ~ line “cavity” L = Cross-section of mode: DC + B 5 µm E 6 GHz in - ++ - Lumped element equivalent circuit 9 Blais, Huang, Wallraff, SMG & RS, PRA 2004 10 µm Advantages of 1d Cavity and Artificial Atom gd= iE/ Vacuum fields: Transition dipole: zero-point energy confined de~40,000 a in < 10-6 cubic wavelengths 0 10 x larger than E ~ 0.25 V/m vs. ~ 1 mV/m for 3-d Rydberg atom cm 2.5 λ ~ L = 10 µm Cooper-pair box “atom” 10 Resonator as Harmonic Oscillator 1122 L r C H =+()LI CV r 22L Φ ≡ LI = momentum ˆ † 1 V = coordinate Hacavity =+ωr ()a2 † VV=+RMS ()aa 112 ⎛⎞1 CV00= ⎜⎟ω 22⎝⎠2 ω V = r ∼ 12− µV RMS 2C 11 Implementation of Cavities for cQED Superconducting coplanar waveguide transmission line Q > 600,000 @ 0.025 K Optical lithography 1 cm at Yale Niobium films gap = mirror 6 GHz: ω = 300mK nmγ 1@20K • Internal losses negligible – Q dominated by coupling 12 The Chip for Circuit QED Nb Nb the ‘atom’ Nb no wires attached to qubit! 13 Superconducting Tunnel Junction as a Covalently Bonded Diatomic ‘Molecule’ (simplified view) N +1 pairs aluminum island N pairs N ∼ 108 tunnel barrier ∼ 1mµ N pairs aluminum island N +1 pairs Cooper Pair Josephson Tunneling Splits the Bonding and Anti-bonding ‘Molecular Orbitals’ anti-bonding bonding 14 Bonding Anti-bonding Splitting 8 1 10 +1 108 ψ =±8 8 ()10 10 +1 ± 2 EEanti-bonding −=bonding EJ ∼∼7 GHz 0.3 K Josephson coupling ↑= bonding E H =− J σ z ↓= anti-bonding 2 15 Dipole Moment of the Cooper-Pair Box (determines polarizability) Vg -- L = 10 µm C1 ---- 1 nm EL=Vg / C ++++ 2 C Vg ++ 3 0 1/C de= (2 )L 2 1/CC12++1/ 1/C3 ↑= bonding EJ z d x H =− σ − Vgσ de~2 -µm ↓= anti-bonding 2 L 16 Energy, Charge, and Capacitance of the CPB ↓ E E zxd J HV=− J σ − σ ↑ g Energy 2 L ↓ no charge dE signal Q = charge Charge ↑ dV ↑ dQ polarizability is C = state dependent ↓ dV Capacitance CV / e 01 2 gg deg. pt. = coherence sweet spot 17 Using the cavity to measure the state of the ‘atom’ E d † HV=− J σ zx− σ VV=+V ()a+a 2 L dc RMS (2e) 1/C2 gV= RMS 1/CC12++1/ 1/C3 V 0 State dependent polarizability of ‘atom’ pulls the cavity frequency18 Dispersive Regime Large Detuning of Atom from Cavity ∆=ω01 −ωr g 19 ω01 z ††− + Ha=− σ +ωσR a+g()a+aσ 2 Large ⎧ g ⎛⎞+ † − ⎫ Detuning of Ua=−exp ⎨ ⎜⎟σσa⎬ Atom from ⎩⎭∆ ⎝⎠ Cavity † Heff = UHU ∆ =−ω01 ωr g 22 ⎛⎞gg† 1⎛⎞ Haeff ≈−⎜⎟ωrzσωa−⎜01 +⎟σz ⎝⎠∆∆2⎝⎠ cavity freq. shift Lamb shift 20 QND : [Heff ,σ z ] = 0 Cavity Transmission Phase Controlled by State of Atom Nb resonator 20 mK ↑ ↓ Linewidth νr = 6.04133 GHz Q = 2πν/κ ~ 10,000 κ=2π x 0.6MHz r κ-1 = 250 ns 21 QND Measurement of Qubit: Dispersive case ν01 ∆ =−2(π ν 01 ν r ) ∆ ν = 6.04133 GHz ν r r EhJ / ∆min ~ 300 MHz (∼ 0.05ν r !) δθκ= 2/g 2 ∆°~5 δθ ~5° min g /π = 5HM z 0 Phase Shift vacuum Rabi frequency 22 Gate Sweep with Qubit Crossing Resonator ∆ = 0 tune qubit thru resonance w/ ν r cavity EhJ / phase shift 0 changes sign at resonance Phase Shift (a.u.) 23 Spectroscopy of Qubit in Cavity Send in 2 frequencies •Readout ν01 •Spectroscopy νr νs Probe (CW) cavity at ν r ↑ 0 -10 Phase ↓ -20 -30 n -40 g Attn (dB) Data -50 1 5.6 5.8 6.0 6.2 6.4 Spectroscopy (CW) Phase at 6.3 GHz near ν01 24 ng Spectrum of Qubit E d HV=− J σ zx− σ 2 L g Vg Cavity Phase EJ Energy Spec Frequency (GHz) 1 nCgg= Vg / e CgVg n = 25 g e Using Cavity to Map Qubit Parameter Space ∆ =−ω01 ωr Transition frequency of qubit Cavity phase shift 2 Φ / Φ 0 ∆ > 0 Φ /Φ 0 ∆ > 0 1 ∆ = 0 Φ0 0 ∆ < 0 ∆ < 0 (GHz) 2e 01 ν 0 1 2 3 4 C V Slice at ∆=0 n = g g g C V e n = g g g e max EEJC~ 6.7 GHz ~ 5.25 GHz 26 Probe Beam at Cavity Frequency Induces ‘Light Shift’ of Atom Frequency 22 ⎛⎞gg† 1⎛⎞ Haeff ≈−⎜⎟ωrzσωa−⎜01 +⎟σz ⎝⎠∆∆2⎝⎠ cavity freq. shift Lamb shift atom ac Stark shift vacuum ac Stark shift (light shift) =×2n cavity pull 11⎛⎞g2 ⎡⎤ Ha≈−ω ††aωσ+2 aa+ eff r ⎜⎟01 ⎢⎥z 22⎝⎠∆ ⎣⎦ 27 Atom ac Stark Shift (Light Shift) Induced by Cavity Photons navg photons 0 50 100 6.2 6.19 20 6.18 GHz Linewidths 0 6.17 Ν 10 450kHz/photon 0 6.16 ΝΝ 6.15 0 0 20 40 60 80 100 RF Power ΜW 28 Measurement Induced Dephasing: back action = quantum noise in the light Shift 11⎛⎞g 2 ⎡⎤ Ha≈−ω ††aωσ+2 aa+ eff r ⎜⎟01 ⎢⎥z 22⎝⎠∆ ⎣⎦ κ − ||τ n fluctuations 2 δτnnˆˆ()δ = ne in photon number 29 Measurement Back Action: Quantum Noise in ac Stark Shift 11⎛⎞g2 ⎡⎤ Ha≈+ω ††aωσ+2 aa+ eff r ⎜⎟01 ⎢⎥z 22⎝⎠∆ ⎣⎦ 1 −+it[(ωϕ01 t)] ψ =↓( +e ↑) 2 2g 2 ⎡ t ⎤ ϕ()tn=+⎢ ∫ dτδnˆ(τ)⎥ ∆ ⎣ 0 ⎦ light shift random dephasing 30 Measurement Back Action: Quantum Noise in ac Stark Shift 2g 2 t δϕτ()td= ∫ δnˆ(τ) ∆ 0 1 − δϕ 2 ()t eeitδϕ () ≈ 2 Assuming gaussian fluctuations 2 2 tt 2 ⎛⎞2g δϕτ()td= ⎜⎟∫∫dτ'δnˆˆ(τ)δn(τ') ⎝⎠∆ 00 31 Measurement Back Action: Quantum Noise in ac Stark Shift Coherent state in driven cavity with damping rate κ κ − ||τ δτnnˆˆ()δ(0)= ne2 τ 32 Measurement Back Action: Quantum Noise in ac Stark Shift 2 2 tt κ −−|'ττ| 2 ⎛⎞2g δϕ ()td= ⎜⎟∫∫τ dτ 'ne2 ⎝⎠∆ 00 2 2 ⎛⎞2g 2 ≈ ⎜⎟nt κt1 ⎝⎠∆ (Gaussian inhomogeneous broadening) 2 ⎛⎞24g 2 ≈ ⎜⎟ntκt1 ⎝⎠∆ κ (phase random walks--phase diffusion) (Lorentzian homogeneous broadening) 33 Qubit Phase Diffusion (weak measurement) 2 2 2 ⎛⎞24g δϕ ()tn≈ ⎜⎟ t ⎝⎠∆ κ 1 2 2 − ϕ 2 ()t ⎡⎤ −itϕ () ⎛⎞2g −Γ t ee==2 exp ⎢⎥−2⎜⎟nκ t=eϕ κ∆ ⎣⎦⎢⎥⎝⎠ 11⎧⎫∞ Γ S(ω) =− Im -i dt eitω e−Γϕt = ϕ ⎨⎬∫ 22 ππ⎩⎭0 ()ω−ω0 +Γϕ Γ∝ϕ n valid for Γϕ κ Measurement induced dephasing rate 34 Qubit Inhomogeneous Broadening (strong measurement) 112 2 −−ϕ 2 ()tt⎡⎤(Γ)2 −itϕ () 12⎛⎞g 2 ϕ ee==22exp ⎢⎥−⎜⎟nt=e 2 ∆ ⎣⎦⎢⎥⎝⎠ Γ∝ϕ n 2 ()ωω− 0 ∞ 1 2 − −Γ()t 2 11⎧⎫it ϕ 2Γ Se(ω) =− Im ⎨⎬-i∫ dt e ω e 2 = ϕ π ⎩⎭0 2π Γϕ Γ∝ϕ n valid for Γϕ κ 35 Measurement Induced Dephasing: back action = quantum noise in the light Shift 11⎛⎞g 2 ⎡⎤ Ha≈−ω ††aωσ+2 aa+ eff r ⎜⎟01 ⎢⎥z 22⎝⎠∆ ⎣⎦ κ − ||τ n fluctuations 2 δτnnˆˆ()δ = ne in photon number Γ∝ϕ n Gaussian Lorentzian Γ∝ϕ n 36 Summary of Dispersive Regime Results Every thing works as predicted except the cavity enhanced lifetime has not been observed. Non-radiative decay channels? ε -glassy losses in oxide barriers loss tangent 2 ∼ 10-4 ε1 -electroacoustic coupling to phonons? (Ioffe, Blatter) 37 Dressed Artificial Atom: Resonant Case ? T ω01 = ωR T 2g γ +κ 2 Fourier transform of Haroche 1 ω /38ω Rabi flopping expt. “vacuum Rabi splitting” R First Observation of Vacuum Rabi Splitting for a Single Atom (on average) Cs atom in an optical cavity photons Thompson, Rempe, & Kimble 199239 First Observation of Vacuum Rabi Splitting in a Superconducting Circuit qubitqubitdetuneddetuned Pprobe =−140 dBm fromfrom cavity cavity = 10−17 W = n ωrκ /2 n ≤ 1 qubit tuned into 2g 2g /2π = 12 MHz resonance 1 1 κ /2π = 0.6 MHz ()qubit + photon ()qubit − photon 2 2 γ /2π = 1 MHz 40 Observing the Avoided Crossing of “Atom” & “Photon” EJr= ω EJr< ω 41 Quantum Computation and NMR of a Single ‘Spin’ Single Spin ½ Quantum Measurement Vds C C C gb Box c ge Vgb Vge SET 42 (After Konrad Lehnert) Quantum control of qubits NMR language z y x microwave pulse 1 Ω1 0 π/2 π pulse pulse free evolution (analogous to gyroscopic precession) NOT NOT43 Rabi Flopping of Qubit Under Continuous Measurement 44 FUTURE DIRECTIONS - strongly non-linear devices for microwave quantum optics - single atom optical bistability - photon `blockade’ - single photon microwave detectors - single photon microwave sources - quantum computation - QND dispersive readout of qubit state via cavity - resonator as ‘bus’ coupling many qubits - cavity enhanced qubit lifetime 45 SUMMARY Cavity Quantum Electrodynamics cQED “circuit QED” Coupling a Superconducting Qubit to a Single Photon -first observation of vacuum Rabi splitting 46 -initial quantum control results Coupling Qubits via Cavity Mode multiple CPB qubits in a cavity Nb Nb 20 µm Nb can integrate multiple qubits in a single cavity,
Load more

Recommended publications
  • Machine Learning for Designing Fast Quantum Gates
    University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2016-01-26 Machine Learning for Designing Fast Quantum Gates Zahedinejad, Ehsan Zahedinejad, E. (2016). Machine Learning for Designing Fast Quantum Gates (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/26805 http://hdl.handle.net/11023/2780 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY Machine Learning for Designing Fast Quantum Gates by Ehsan Zahedinejad A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN PHYSICS AND ASTRONOMY CALGARY, ALBERTA January, 2016 c Ehsan Zahedinejad 2016 Abstract Fault-tolerant quantum computing requires encoding the quantum information into logical qubits and performing the quantum information processing in a code-space. Quantum error correction codes, then, can be employed to diagnose and remove the possible errors in the quantum information, thereby avoiding the loss of information. Although a series of single- and two-qubit gates can be employed to construct a quan- tum error correcting circuit, however this decomposition approach is not practically desirable because it leads to circuits with long operation times. An alternative ap- proach to designing a fast quantum circuit is to design quantum gates that act on a multi-qubit gate.
    [Show full text]
  • Dr. Julien BASSET Maître De Conférences (Lecturer)
    Dr. Julien BASSET Maître de Conférences (Lecturer) Université Paris Sud Laboratoire de Physique des Solides Nanostructures at the Nanosecond group Bat 510 FR - 91405 Orsay France +33 1 69 15 80 11 [email protected] https://www.equipes.lps.u-psud.fr/ns2 Work Experience September University Lecturer in Experimental Condensed Matter Physics 2014– at Université Paris Sud XI Today Nanostructures at the nanosecond group - Laboratory for Solid State Physics, Orsay, France December Post-Doc in Experimental Condensed Matter Physics: “Dipole 2011– coupling semiconductor double quantum dots to microwave res- August onators: coherence properties and photon emission” 2014 Klaus ENSSLIN’s and Andreas WALLRAFF’s quantum physics groups (Joint project) - Laboratory for Solid State Physics (ETH Zürich) Zürich, Switzerland October PhD Thesis in Experimental Condensed Matter Physics: “High 2008 – frequency quantum noise of mesoscopic systems and current- October phase relation of hybrid junctions” 2011 Hélène BOUCHIAT’s and Richard DEBLOCK’s mesoscopic physics group - Laboratoire de Physique des Solides (CNRS - Université Paris Sud XI) Orsay, France • Jury members : – Referee: Silvano De Franceschi (CEA Grenoble) – Referee: Norman Birge (Michigan State University) – Examiner: Benoît Douçot (LPTHE Paris ) – Examiner: Christian Glattli (CEA Saclay) – President: Pascal Simon (Université Paris Sud) – Thesis co-director: Hélène Bouchiat (LPS Orsay) – Thesis co-director: Richard Deblock (LPS Orsay) March Researcher Assistant (3 months): : “Spin transfer
    [Show full text]
  • Quantum Information with Superconducting Circuits Benjamin Huard
    Quantum information with superconducting circuits Benjamin Huard To cite this version: Benjamin Huard. Quantum information with superconducting circuits. Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]. Ecole Normale Supérieure de Paris - ENS Paris, 2014.tel- 01011096 HAL Id: tel-01011096 https://tel.archives-ouvertes.fr/tel-01011096 Submitted on 26 Jun 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. D´epartement de Physique Ecole´ Normale Sup´erieure ÉCOLE NORMALE SUPÉRIEURE M´emoire d’habilitation `adiriger des recherches Benjamin Huard Circuits supraconducteurs pour l’information quantique qui sera d´efendue le 16 juin 2014 devant le jury compos´ede : M. Olivier Buisson .................. Rapporteur M. David DiVincenzo ................ Rapporteur M. Jean-Michel Raimond ........... Examinateur M. Jakob Reichel .................... Examinateur M. Andreas Wallraff ................ Rapporteur Acknowledgements I would like to thank here all the people I had the luck to interact with since I’m a physicist and who contributed directly or not to the work presented in this manuscript. I have fond memories of my time in the Quantronics group at Saclay, where it was a great pleasure to work everyday with such a talented, friendly and upright set of people.
    [Show full text]
  • Superconducting Qubits: Dephasing and Quantum Chemistry
    UNIVERSITY of CALIFORNIA Santa Barbara Superconducting Qubits: Dephasing and Quantum Chemistry A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics by Peter James Joyce O'Malley Committee in charge: Professor John Martinis, Chair Professor David Weld Professor Chetan Nayak June 2016 The dissertation of Peter James Joyce O'Malley is approved: Professor David Weld Professor Chetan Nayak Professor John Martinis, Chair June 2016 Copyright c 2016 by Peter James Joyce O'Malley v vi Any work that aims to further human knowledge is inherently dedicated to future generations. There is one particular member of the next generation to which I dedicate this particular work. vii viii Acknowledgements It is a truth universally acknowledged that a dissertation is not the work of a single person. Without John Martinis, of course, this work would not exist in any form. I will be eter- nally indebted to him for ideas, guidance, resources, and|perhaps most importantly| assembling a truly great group of people to surround myself with. To these people I must extend my gratitude, insufficient though it may be; thank you for helping me as I ventured away from superconducting qubits and welcoming me back as I returned. While the nature of a university research group is to always be in flux, this group is lucky enough to have the possibility to continue to work together to build something great, and perhaps an order of magnitude luckier that we should wish to remain so. It has been an honor. Also indispensable on this journey have been all the members of the physics depart- ment who have provided the support I needed (and PCS, I apologize for repeatedly ending up, somehow, on your naughty list).
    [Show full text]
  • Entanglement Stabilization Using Parity Detection and Real-Time Feedback in Superconducting Circuits Science Team: C
    Entanglement Stabilization using Parity Detection and Real-Time Feedback in Superconducting Circuits Science Team: C. Andersen, S. Balasiu, J.-C. Besse, M. Collodo, J. Heinsoo, J. Herrmann, S. Krinner, P. Kurpiers, P. Magnard, G. Norris, A. Remm, P. Scarlino, T. Walter, C. Eichler, A. Wallraff (ETH Zurich) B. Royer, and A. Blais (Université de Sherbrooke) Technical Team: A. Akin, M. Frey, M. Gabureac, J. Luetolf Andreas Wallraff, Quantum Device Lab | 29-Apr-19 | 13 Acknowledgements www.qudev.ethz.ch Former group members now K. Juliusson (CEA Saclay) Collaborations (last 5 years) Faculty/PostDoc/PhD/Industry C. Lang (Radionor) with groups of A. Abdumalikov (Gorba AG) P. Leek (Oxford) A. Bachtold (ICFO Barcelona) E. Solano (UPV/EHU) M. Allan (Leiden) P. Maurer (Chicago) A. Blais (Sherbrooke) H. Tureci (Princeton) M. Baur (ABB) J. Mlynek (Siemens) A. Chin (Cambridge) W. Wegscheider (ETH Zurich) J. Basset (U. Paris Sud) M. Mondal (IACS Kolkata) M. Delgado (UC Madrid) S. Berger (AWK Group) M. Oppliger L. DiCarlo (TU Delft) R. Bianchetti (ABB) M. Pechal (Stanford) P. Domokos (WRC Budapest) D. Bozyigit (MIT) A. Potocnik (imec), K. Ensslin (ETH Zurich) A. Fedorov (UQ Brisbane) G. Puebla (IBM Zurich) J. Faist (ETH Zurich) A. Fragner (Yale) A. Safavi-Naeini (Stanford) A. Fedorov (Brisbane) S. Filipp (IBM Zurich) Y. Salathe (Zurich Inst.) K. Hammerer (Hannover) J. Fink (IST Austria) M. Stammeier (Huba Control) M. Hartmann (Hariot Watt) T. Frey (Bosch) L. Steffen (AWK Group) T. Ihn (ETH Zurich) S. Garcia (College de France) A. Stockklauser (Rigetti) F. Merkt (ETH Zurich) S. Gasparinetti (Chalmers) T. Thiele (UC Boulder, JILA) L.
    [Show full text]
  • ROBERT J. SCHOELKOPF Yale University
    ROBERT J. SCHOELKOPF Yale University Phone: (203) 432-4289 15 Prospect Street, #423 Becton Center Fax: (203) 432-4283 New Haven, CT 06520-8284 e-mail: [email protected] website: http://rsl.yale.edu/ PERSONAL U.S. Citizen. Married, two children. EDUCATION Princeton University, A. B. Physics, cum laude. 1986 California Institute of Technology, Ph.D., Physics. 1995 ACADEMIC APPOINTMENTS Director of Yale Quantum Institute 2014 – present Sterling Professor of Applied Physics and Physics, Yale University 2013- present William A. Norton Professor of Applied Physics and Physics, Yale University 2009-2013 Co-Director of Yale Center for Microelectronic Materials and Structures 2006-2012 Associate Director, Yale Institute for Nanoscience and Quantum Engineering 2009 Professor of Applied Physics and Physics, Yale University 2003-2008 Interim Department Chairman, Applied Physics, Yale University July-December 2012 Visiting Professor, University of New South Wales, Australia March-June 2008 Assistant Professor of Applied Physics and Physics, Yale University July 1998-July 2003 Associate Research Scientist and Lecturer, January 1995-July 1998 Department of Applied Physics, Yale University Graduate Research Assistant, Physics, California Institute of Technology 1988-1994 Electrical/Cryogenic Engineer, Laboratory for High-Energy Astrophysics, NASA/Goddard Space Flight Center 1986-1988 HONORS AND AWARDS Connecticut Medal of Science (The Connecticut Academy of Science and Engineering) 2017 Elected to American Academy of Arts and Sciences 2016 Elected to National Academy of Sciences 2015 Max Planck Forschungspreis 2014 Fritz London Memorial Prize 2014 John Stewart Bell Prize 2013 Yale Science and Engineering Association (YSEA) Award for Advancement 2010 of Basic and Applied Science Member of Connecticut Academy of Science and Engineering 2009 APS Joseph F.
    [Show full text]
  • Circuit Quantum Electrodynamics
    REVIEWS OF MODERN PHYSICS, VOLUME 93, APRIL–JUNE 2021 Circuit quantum electrodynamics Alexandre Blais Institut quantique and D´epartement de Physique, Universit´e de Sherbrooke, Sherbrooke, Qu´ebec J1K 2R1, Canada and Canadian Institute for Advanced Research, Toronto M5G 1M1, Ontario, Canada Arne L. Grimsmo Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia S. M. Girvin Yale Quantum Institute, P.O. Box 208 334, New Haven, Connecticut 06520-8263, USA Andreas Wallraff Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland and Quantum Center, ETH Zurich, CH-8093 Zurich, Switzerland (published 19 May 2021) Quantum-mechanical effects at the macroscopic level were first explored in Josephson-junction- based superconducting circuits in the 1980s. In recent decades, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to gate-based digital quantum information processing with superconducting circuits. In addition, circuit QED provides a framework for the study of hybrid quantum systems, such as quantum dots, magnons, Rydberg atoms, surface acoustic waves, and mechanical systems interacting with microwave photons.
    [Show full text]
  • Circuit Quantum Electrodynamics (QED)
    Circuit Quantum Electrodynamics (QED) David Haviland Erik Tholen Jochen Walter Adem Ergul Frank Weber Evelyn Dorthy Nanostructure Physics, Dept. Applied Physics, KTH, Albanova Atom in a Cavity Consider only two levels of atom, with energy separation hΩ Atom drifts through electromagnetic resonant cavity with very high Q Jaynes-Cummings Hamiltonian: Strong Coupling limit Needed: g >> κ,γ High Q decay rate to nonmodes -γ cavity- Large d Blais et. al, Phys. Rev. A, 2004 Electropolished superconducting Nb cavity 50 mm diameter and a 40 mm radius of curvature Nice presentation at: http://www.lkb.ens.fr/recherche/qedcav/english/englishframes.html Energy Eigenstates Neglect damping for the moment, exact diagonalization gives energy eigenstates: For zero detuning the degeneracy of the photon states with the atom state is lifted by the coupling. These “dressed states” are “maximally entangled” atom – field states Blais et. al, Phys. Rev. A, 2004 Spectrum Vacuum Rabi flopping: ↓ 0, ↑ 1, 0 photons in cavity atom in GS atom in excited state 1 photon in cavity Cavity photon number Atom Atom ground excited state state Level splitting depends on number of photons in cavity 2g n+ 1 Blais et. al, Phys. Rev. A, 2004 Splitting of Cavity Resonance κ + γ Now consider damping: excitation is ½ photon, ½ atom ⇒ decay rate: 2 In strong coupling limit there is a splitting of cavity resonance which can be resolved because: ε d =g rms >>κ, γ h Blais et. al, Phys. Rev. A, 2004 CP box in Microstrip line cavity Very small effective volume, ~10-5 cubic wavelengths Blais et. al, Phys.
    [Show full text]
  • Design of an Inductively Shunted Transmon Qubit with Tunable Transverse and Longitudinal Coupling
    DESIGN OF AN INDUCTIVELY SHUNTED TRANSMON QUBIT WITH TUNABLE TRANSVERSE AND LONGITUDINAL COUPLING Von der Fakult¨atf¨urMathematik, Informatik und Naturwissenschaften der RWTH Aachen University genehmigte Dissertation zur Erlangung des akademischen Grades einer Doktorin der Naturwissenschaften vorgelegt von M. Sc. Susanne Richer aus Bocholt Berichter: Prof. Dr. David DiVincenzo Dr. Ioan Pop Prof. Dr. Christoph Stampfer Tag der m¨undlichen Pr¨ufung:28. Februar 2018 Diese Dissertation ist auf den Internetseiten der Universit¨atsbibliothek verf¨ugbar. ABSTRACT Superconducting qubits are among the most promising and versatile build- ing blocks on the road to a functioning quantum computer. One of the main challenges in superconducting qubit architectures is to couple qubits in a well-controlled manner, especially in circuit constructions that in- volve many qubits. In order to avoid unwanted cross-couplings, qubits are oftentimes coupled via harmonic resonators, which act as buses that mediate the interaction. This thesis is set in the framework of superconducting transmon-type qubit architectures with special focus on two important types of coupling between qubits and harmonic resonators: transverse and longitudinal coupling. While transverse coupling naturally appears in transmon-like circuit constructions, longitudinal coupling is much harder to implement and hardly ever the only coupling term present. Nevertheless, we will see that longitudinal coupling offers some remarkable advantages with respect to scalability and readout. This thesis will focus on a design, which combines both these coupling types in a single circuit and provides the possibility to choose between pure transverse and pure longitudinal or have both at the same time. The ability to choose between transverse and longitudinal coupling in the same circuit provides the flexibility to use one for coupling to the next qubit and one for readout, or vice versa.
    [Show full text]
  • Demonstration of an All-Microwave Controlled-Phase Gate Between Far Detuned Qubits
    Demonstration of an All-Microwave Controlled-Phase Gate between Far Detuned Qubits S. Krinner,1, ∗ P. Kurpiers,1, † B. Royer,2, 3 P. Magnard,1 I. Tsitsilin,1, 4 J.-C. Besse,1 A. Remm,1 A. Blais,2, 5 and A. Wallraff1, ‡ 1Department of Physics, ETH Zurich, 8093 Zurich, Switzerland 2Institut Quantique and Départment de Physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada 3Department of Physics, Yale University, New Haven, Connecticut 06520, USA 4Russian Quantum Center, National University of Science and Technology MISIS, Moscow 119049, Russia 5Canadian Institute for Advanced Research, Toronto, Canada (Dated: June 19, 2020) A challenge in building large-scale superconducting quantum processors is to find the right balance between coherence, qubit addressability, qubit-qubit coupling strength, circuit complexity and the number of required control lines. Leading all-microwave approaches for coupling two qubits require comparatively few control lines and benefit from high coherence but suffer from frequency crowding and limited addressability in multi-qubit settings. Here, we overcome these limitations by realizing an all-microwave controlled-phase gate between two transversely coupled transmon qubits which are far detuned compared to the qubit anharmonicity. The gate is activated by applying a single, strong microwave tone to one of the qubits, inducing a coupling between the two-qubit |f, gi and |g, ei states, with |gi, |ei, and |fi denoting the lowest energy states of a transmon qubit. Interleaved randomized benchmarking yields a gate fidelity of 97.5 ± 0.3% at a gate duration of 126 ns, with the dominant error source being decoherence. We model the gate in presence of the strong drive field using Floquet theory and find good agreement with our data.
    [Show full text]
  • Press Dossier
    Press Dossier Quantum Flagship Kick-off Event Vienna, October 29-30, 2018 All information in this press dossier is Embargoed until Monday October 29th at 12:00pm CET Index The Quantum Flagship (QF) ........................................................................................................................ 3 The Goals of the QF ................................................................................................................................. 4 The Activities of the QF ........................................................................................................................ 4 The Pillars ................................................................................................................................................... 5 QSA Team - Quantum Flagship .................................................................................................................. 6 Selected projects ............................................................................................................................................... 7 Spokespersons Individual Projects ........................................................................................................ 8 Quantum Community Network ................................................................................................................. 25 The Quantum Flagship The Quantum Flagship was launched in 2018 area as well as to transfer quantum physics as one of the largest and most ambitious research from the lab to the market
    [Show full text]
  • Pulsed Reset Protocol for Fixed-Frequency Superconducting
    Pulsed reset protocol for fixed-frequency superconducting qubits D. J. Egger, M. Werninghaus, M. Ganzhorn, G. Salis, A. Fuhrer, P. Müller, S. Filipp IBM Research GmbH, Zurich Research Laboratory, Säumerstrasse 4, 8803 Rüschlikon, Switzerland (Dated: April 2, 2019) Improving coherence times of quantum bits is a fundamental challenge in the field of quantum computing. With long-lived qubits it becomes, however, inefficient to wait until the qubits have relaxed to their ground state after completion of an experiment. Moreover, for error-correction schemes it is important to rapidly re-initialize syndrome qubits. We present a simple pulsed qubit reset protocol based on a two-pulse sequence. A first pulse transfers the excited state population to a higher excited qubit state and a second pulse into a lossy environment provided by a low-Q transmission line resonator, which is also used for qubit readout. We show that the remaining excited state population can be suppressed to 1:7 ± 0:1% and that this figure may be reduced by further improving the pulse calibration. INTRODUCTION rapidly tuned into resonance [16], a scheme that is also used for generating traveling single-photon Fock-states Building a fully operational and useful quantum com- [17, 18]. When the qubit frequency cannot be tuned in- puter requires many good, high-coherence qubits along situ [19] and the coupling between qubits and other cir- with high-fidelity gates. An equally important require- cuits is fixed, coherent microwave pulses provide the only ment is the ability to (re-)initialize qubits in their ground way to manipulate the system.
    [Show full text]