Noise and decoherence in the Josephson Charge Qubits Oleg Astafiev, Yuri Pashkin, Tsuyoshi Yamamoto, Yasunobu Nakamura, Jaw-Shen Tsai RIKEN Frontier Research System NEC Fundamental Research Laboratories

Outline The Josephson charge qubit Single-shot readout with charge trap Measurements of energy relaxation Charge fluctuators and energy relaxation

The Josephson Charge Qubit Charging energy (for Cooper pair): Josephson energy: EJEJ EJEJ C b >> C g E n g =V g C g /e         Reservoir Box CbCb CgCg 2e22e2 CbCb Control gate n g = VgCgVgCg e Degeneracy >> kT 2e22e2 CbCb >> E J 02314

The Hamiltonian Eigenstates Eigenenergies

|0  |1  t = 0: t > 0: Coherent Oscillations P tt 1 0 E tt   |1  2   |1  2  -pulse:  J  t =  q EJEJ

Cooper-Pair Box GateGate ＳＱＵＩＤＳＱＵＩＤ ProbeJunctionProbeJunction 1m1m ProbeJunctionProbeJunction Cooper- pair Box Cooper- GateGate ＳＱＵＩＤＳＱＵＩＤ Al/AlO x /Al tunnel junctions Pulse induced current in SQUID – box – probe junction circuit is measured  0  +  1  I = 2e |  | 2 /T r TrTr Control pulse sequence  t (ns) 0 1

2e Cooper-pair box Final state read-out A pair of qusiparticles tunnels through the probe junction biased to V b  2  /e e e + probe

Single-shot Readout Coherent oscillations Quasiparticle tanneling (when the trap is biased to 2  /e) Reservoir Box Control gate qubit CbCb C ts SET Readout circuit CsCs I C bt Trap Readout gate CtCt t readout: control: Pulses

Measurement circuit is electrostatically decoupled from the qubit Final states are read out after termination coherent state manipulation

Reservoir Box SET Trap gate Readout with control  -pulses Readout pulse Control  -pulse ngng I

tt (ns) b P Quantum Oscillations  q (e)  =  /   -pulse Degeneracy Crossection tt qq

Relaxation to the reservoir Readout tdtd Control  -pulse 220 exp(-t/288)+32 T1 res = 288 ns N tot = 327 Reservoir Box SET Trap

Relaxation to the Trap Control  -pulse t width T eff = (1/T 1 res + 1/T 1 trap ) -1 = 31 ns Readout Reservoir Box SET Trap

Readout efficiency Reservoir Box SET Trap

Two-level System as a Quantum Noise Spectrometer Two-level system TLS Environment Electrostatic energy noise Charge basis: Eigenbasis: tan  = EJEJ E UU EJEJ  UU z x transitions dephasing Dephasing Transitions UU UU   sincos 2 xzz tU E H  E

Charge qubit qq charge noise spectral density: S q (  ) S U (  ) = (2e/C) 2 S q (  )  1 = 2222  SU() SU() Relaxation rate: sin 2  Dephasing: SUSU Dephasing Relaxation Excitation 

T 1 time measurements ngng E tata P(1)  exp(-t a /T 1 ) time readout pulse Control  -pulse Adiabatic pulse

Degeneracy T 1 time vs Gate Voltage

E J -dependences Degeneracy Off degeneracy

Coupling to Environment through Electrical Leads Coupling to gates: Coupling to SET: Measured relaxation time can not be explained by coupling to the external environment through electrical leads

Effect of the measurement SET

The noise derived from  1 time  1 = 2222  SU(0) SU(0) sin 2 

T 2 -2

Classical  Quantum Noise Quantum f-noise (  > 0): Classical 1/f-noise:   (kT eff ) 2  Do low frequency 1/f and high frequency f noises have common origin?  1/f  f SU()SU() kT/   emissionabsorption

Relaxation through Fluctuators Dephasing is caused by 1/f noise of charge fluctuators with activation energy less than kT Fluctuators with activation energy of   (   >> kT) accept qubit excess energy kT EE

Low frequency 1/f noise

Temperature dependences of the 1/f noise

Standard qubit on 400 nm thick Si 3 N 4

1/f noise in superconducting – normal SETs

SET on GaAs substrate

SET on Al 2 O 3 Si Al Al 2 O 3 SET island

Large area SETs

1/f noise properties from experiments does not depend on substrate type noise appears in oxide of Al(?) scales with SET size (area?) saturation level at low temperatures depends on current

Basic properties of the 1/f noise caused by bistable fluctuators    S()S()

Qubit TLS (fluctuators) Environment at T > 0  Qubit island TLS fluctuators The qubit is coupled to environment through charge degree of freedom

1/f noise  23  Environment at T > 0 high frequency cutoff of the 1/f noise If, then

1 2 3 Qubit relaxation (excitation)

1/f low frequency noise: f high frequency noise: Crossover frequency:

Same fluctuators contribute in the 1/f noise and the quantum f noise Constant distribution of two energy parameters for the fluctuators is required

Two energy parameters: Single energy:

Single energy (TLS)  Environment at T > 0 00 High frequency cutoff 1/f noise:  << kT f noise:     < 10 5 Hz    Hz Different TLS contribute in 1/f and f noises

Conclusion  We have demonstrated single-shot readout using charge trap  Energy relaxation of the qubit has been measured  The energy relaxation is caused by quantum f noise which has crossover frequency with 1/f noise at kT/   Nearly T 2 dependence of the 1/f noise has been observed