Depts. of Applied Physics & Physics Yale University expt. K. Lehnert L. Spietz D. Schuster B. Turek Chalmers University K.Bladh D. Gunnarsson P. Delsing The Cooper-pair Box as a Quantum Spectrum Analyzer Rob Schoelkopf The David and Lucile Packard Foundation Funding: And discussions w/: M. Devoret & J. Martinis theory A. Clerk S. Girvin D. Stone Yale

Cooper-pair Box Coupled to an SET Box SET VgVg V ge CgCg CcCc C ge V ds BoxSET Electrometer Superconducting tunnel junction Qubit Quantum state readout Quantum spectrum analyzer Cooper-pair Box SET Transistor Nonequilibrium noise source or

Cooper-pair Box VgVg VgVg (e.g. Bouchiat et al., 98)

E Cooper-pair Box as Quasi-spin 1/2 Measure charge Excited state Ground state a bc a bc abc

Continuous Measurement of a Single Spin Measured continuously by SET Theory: Cooper-pair box ground state 2e 1e Measurement must cause additional dephasing uncertainty principle Measurement may also mix states, drive transitions from ground state 1

E Cooper-Pair Resonance Spectroscopy V app  =38 GHz CgCg V app =V g +V ac sin  t GHz 2-photon Peak

Peak location E B “SQUID box” to vary E J Fit parameters: Determination of Box Hamiltonian V app 32 GHz 35 GHz 38 GHz

Effects of Voltage Noise on Pseudo-Spin slow fluctuations of dephasing resonant fluctuations of mixing

absorptionemission Emission and Absorption due to Environment Box

CgCg Spontaneous Emission into Environment estimate: Excited-state lifetime, T 1 VgVg

Peak height ( e ) 0time 10  s Excited-state Lifetime Measurement of Box e follow peak height after shift with continuous measurement 76 GHz)

Relaxation by Electrometer? Peak Height (e) Electrometer Operating Point ( V ge ) CgCg 2e2e SET VgVg CcCc e-e- V ge Peaks saturate when

V ds Charging Diagram of SET Electrometer C g V ge /e eV ds V ge Electrometer SET: R = 150 k  E C ~  ~ 2.4 K 44 2E c 0 1e Electrometer operating pt. on “DJQP” feature

Quantum Shot Noise of DJQP* Process ExcitationRelaxation Sharp thresholds due to opening & closing of transport channels ΓΓ *Double Josephson-quasiparticle cycle: (A. Clerk et al. cond-mat/ )

Predicted Effects of DJQP on Box Charge Qubit acts like a spectrum analyzer of the SET quantum noise! (A. Clerk et al. cond-mat/ ) (see also Aguado & Kouwenhoven, 2000 for double dot) 1 0 Average box charge Log[S V (  )] SET noise spectrum on resonance off resonance

Inelastic lifetime is long > 1  s : (and electrometer affects T 1 !) Cooper-pair box as a “quantum spectrum analyzer” RF-SET a good probe of the charge states of box Spectroscopic determination of Hamiltonian of box Conclusions Measures all Noise Classical (symmetric) Quantum (asymmetric) 0

Gap rise (V ds = 1200  V) JQP (V ds = 800  V) Supercurrent (V ds =0) Coulomb Staircase vs. Electrometer Bias T=20 mK Back-action increases with electrometer bias DJQP (V ds = 400  V)

Cooper-pair Staircase vs. Electrometer Bias Theory: Cooper-pair box ground state 2e 1e sweep 2e per 100  s Data: V ds = 350  V V ds = 275  V V ds = 250  V

Cooper-pair Staircase vs. Josephson Coupling Theory: Cooper-pair box w/ max E J 2e 1e Data: maximum E J minimum E J

Peak height B “SQUID box” to vary E J Charge States Coupled by E J V app Peak location 32 GHz 35 GHz 38 GHz

n e =-1n e =0n e =1 EcEc E Single-electron Box: Coulomb Staircase e e Coulomb Staircase Thermally broadened kT/E c mK 200 mK 50 mK 0 1 First demonstrated by Lafarge et al, ’91 (CEA Saclay) E c /4

Temperature Dependence in Normal State

Peak width Decoherence Time of Box GHz78 GHz 0.2

DJQP Noise, Off-resonance  Γ  > Γ  Population inversion in the qubit. Ω / E CS Avg. Qubit Charge Move away from the center of the resonance by increasing V DS … NBNB

Peak height E B “SQUID box” to vary E J Charge States Coupled by E J V app

Effects of Voltage Noise on Qubit x slow fluct. of dephasing resonant fluct. of mixing z

Box State Depends on Electrometer Bias V ds (  V)

CgCg 2e2e SET Box Environment Spontaneous Emission VgVg CcCc V ds E Relaxation

Backaction of SET on Box t CmCm CgCg Z env

Who’s measuring whom? Measured continuously by SET Theory: Cooper-pair box ground state 2e 1e 0 1

Can Electrical Circuits be ‘Quantum?’ Cooper-pair box Y. Nakamura et al, Nature 1999 New Challenges: Understand and minimize decoherence Develop efficient quantum readout New Opportunities: Create artificial atoms Quantum computation Macroscopic Quantum Coherence:

Quantum Circuits for Quantum Computing Classical bit values 0 or 1 Information as state of a two-level quantum system or values, Prediction: a 2,000 bit quantum computer = a conventional computer the size of universe. Quantum bit (or “qubit”) superposition:

0 The Quantum Spectrum Analyzer C meas ? V bias Measures all Noise Classical (symmetric) Quantum (asymmetric)

Quantum Computing Scalable Coherent Controllable Measurable Cooper-pair box SQUID’s Ion Traps Liquid State NMR Nuclear Spins in Semiconductors How coherent is a Cooper-pair box?

Outline Charge quantization on a normal-metal island Single-electron Box Superconducting island as quantum two-level system Cooper-pair Box Spectroscopy of the Cooper-pair box Single-electron Tranistor (SET) measures box Box Measures SET Quantum Spectrum Analyzer

Microwaves Small, Cold and Fast 1  m Dilution refrigerator T = 15 mK Millikelvins Nanometers

Experiment Diagram

Quantum Shot Noise of DJQP* Process Avg. Qubit Charge Hertz NBNB Ω / E CS ExcitationRelaxation Ω= -E CS Ω= E CS  Qubit acts like a spectrum analyzer of the SET quantum noise! *Double Josephson-quasiparticle cycle: (A. Clerk et al. cond-mat ) (see also Aguado & Kouwenhoven, 2000 for double dot)

Single Spin ½Quantum Measurement NMR of a Single Spin Box SET V gb V ge C gb CcCc C ge V ds

e nene The Single-Electron Box n e to n e +1 electrons VgVg island C j R j CgCg n e =-1n e =0n e =1 EcEc E E c /4 Normal tunnel junction

n e =-1n e =0n e =1 EcEc E Single-electron Box: Coulomb Staircase e e Coulomb Staircase Thermally broadened kT/E c mK 200 mK 50 mK 0 1 First demonstrated by Lafarge et al, ’91 (CEA Saclay) E c /4

C ge V ge V ds I ds V ds 10 nA 1 mV Single-electron Transistor: Electrometer Electrometer input gate drain source SET

Quantum Shot Noise of DJQP* Process Hertz Ω / E CS ExcitationRelaxation  Sharp thresholds due to opening & closing of transport channels ΓΓ *Double Josephson-quasiparticle cycle: (A. Clerk et al. cond-mat/ )

10 -5 e/Hz 1/2 charge noise Sub-electron sensitivity for > 100 MHz bandwidth Electrometer input gate Transformer SET RF Reflected power Measure RF power reflected from LC transformer Schoelkopf et al., (Science 1998) Radio-Frequency Single Electron Transistor (RF-SET) Response to step in V ge single time trace

e nene The Single-Electron Box n e to n e +1 electrons VgVg island C j R j CgCg n e =-1n e =0n e =1 EcEc E E c /4 Normal tunnel junction

Conclusions Cooper-pair Box: A quantum two-level system worst-case coherence Box Hamiltonian determined with spectroscopy Long excited-state lifetime while continuously measured.

Gap rise 500 pA Eye 100 pA Weak JQP 100 pA Strong JQP 150 pA Double JQP 300 pA Coulomb Staircase vs. Electrometer Bias T=20 mK Back-action increases with electrometer current