Introducing 3D transmon Hanhee Paik Department of Applied Physics Yale University Experiment W/͛Ɛ Theory
Dave Schuster Lev Bishop Gerhard Kirchmair Luigi Frunzio Adam Sears Steve Girvin Gianluigi Catelani Blake Johnson Leonid Glazman Dong Zhou Matt Reagor Simon Nigg Luyan Sun Michel Devoret Eran Ginossar Matt Reed Leo DiCarlo Rob Schoelkopf Eric Holland Brian Vlastakis Outline
Review : Superconducting qubits, transmon and circuit QED
3D transmon - a transmon in a waveguide cavity : Coherence improved by an order of magnitude
New physics observed in superconducting qubits :
What can T1 and T2 tell us?
How to manipulate 3D transmons? : Single and two qubit gates using microwave driving
Paik et al. Phys. Rev. Lett. 107, 240501 (2011) Superconducting Qubits
Superconductor ZZ01z 12
Z12 1 nm Insulating barrier 1 Z
Energy 01 0 Superconductor (Al)
nonlinearity from Z ~5 10G Hz Josephson junction electromagnetic oscillator 01 (dissipationless)
e2 =2 Charging E Josephson E energy C energy J 2 2C6 4e LJ Interacting with SC qubits: Circuit QED A Circuit Implementation of Cavity QED
2g = vacuum Rabi freq. N = cavity decay rate J с͞ƚƌĂŶƐǀĞƌƐĞ͟ĚĞĐĂLJƌĂƚĞ
Jaynes-Cummings Hamiltonian Z HÖ Z ()aa 1 a VVÖ g()a V a H H r 2 2 z NJ
Quantized Field 2-level system Electric dipole Dissipation Interaction Interacting with SC qubits: Circuit QED A Circuit Implementation of Cavity QED
Strong Coupling = g !NJ
out
Superconducting transmission ůŝŶĞ͞ĐĂǀŝƚLJ͟
10 Pm Superconducting artificial Microwave ͞ĂƚŽŵ͟ in Theory: Blais et al., Phys. Rev. A 69, 062320 (2004) Charge Qubits
superconductor tunnel oxide layer superconductor
V. Bouchiat, D. Vion, P. Joyez, D. Esteve, & M.H. Devoret, Physica Scripta T76, 165 (1998). Transmon : Outsmarting 1/f Charge Noise Cooper-pair Box ͞Transmon͟
Vg
Koch et al., 2007; Houck et al., 2008 T1 can be ~ 10 Ps
EJ/EC = 1 EJ/EC = 25 - 100
Energy Energy sweet exponentially spot suppresses 1/f! Sensitive n = C V /2e to charge noise ng = CgVg/2e g g g Coherence in Conventional Transmon Qubit
T1 1.5Ps Random benchmarking of 1-qubit ops Chow et al. PRL 2009: Technique from Knill et al. for ions
* T21 23.0T Ps Error per gate = 1.2 %
Similar error rates in phase qubits (UCSB): Lucero et al. PRL 100, 247001 (2007) History of Charge Qubit Coherence
Number of gate operation gate Number of
What is limiting coherence? d, YƵĞƐƚŝŽŶ͗tŚĞƌĞ͛Ɛthe Dissipation?
Surface losses?
Substrate losses? ? Junction losses? Radiation? ? ?
Quasiparticles? Shunt capacitance
Which element matters the most? Typical Junction: Dirt Happens
Dolan Bridge Technique Qubit: two 200 x 300 nm junctions
PMMA/MAA bilayer Rn~ 3.5 kOhms Al/AlOx/Al Ic ~ 40 nA Current Density ~ 30- 40 A/cm2 Surfaces Can Matter
E d Nb - + + - 5 Pm D-Al2O3
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even a thin (few nanometer) surface layer will store ~ 1/1000 of the energy
If surface loss tangent is poor ( tanG ~ 10-2) would limit Q ~ 105
as shown in: Increase spacings Gao et al. 2008 (Caltech) decreases energy on surfaces 2¶&RQQHOOHWDO 8&6% increases Q Wang et al. 2009 (UCSB) Recent IBM work by Chow and Colores el at. 2012 How to Reduce the Importance of the Surface
CPW/Compact Resonator* Surface participation ratio t L diel 23 L ~ 10 Pm psurf ~ 10 10
3D L ~ 5,000 Pm diel 6 t L Assume: psurf ~ 0 10 t ~ 3 nm
Use 3D cavity for circuit QED experiment! A High-Q Aluminum Superconducting (3D) Cavity 11.416763635 GHz Aluminum cylindrical ɷf = 19Hz waveguide cavity : TE011 mode Q = 600M (ideally 1 Photon i Zero E field (-175dBm) Q = 510M 10B Photons c On surface) (-77dBm) ĺ QL = 275M
no power dependence of Q : absence of surface dielectric loss M. Reagor, H. Paik et al. in preparation (2012) Rectangular Waveguide Cavity
y0=5 mm
50 mm z0 = 36 mm
x0=18 mm aluminum alloy TE101 fundamental mode (6061-T6, Tc ~ 1.5 K)
Internal Q ~ 5,000,000 with 6061 aluminum alloy : - Q > 30M can be obtained with pure aluminum. Rectangular cavity - lower symmetry than a cylindrical cavity - lower density of modes in the measurement bandwidth Q) How do we couple the qubit to this cavity?
JJ
250 Pm Q) How do we couple the qubit to this cavity? A) Add an antenna!
Single small Al Josephson junction with a short dipole antenna JJ d d a 0.01O
250 Pm Rectangular Waveguide Cavity for circuit QED ͞ϯtransmon͟ single small Al JJ with a short dipole JJ antenna d a 0.01O
250 Pm 50 mm d x E Smaller fields compensated by larger dipole g rms h Still has same net coupling! g a 100 MHz It is a transmon! (only coherence time is longer) Antenna makes E /E ~ 50 to 100 1 MHz j c Lowerging Spec power
Anharmonicity a 300 MHz
Linewidth < 10 kHz 1 T * t15 Ps 2 2S'f All 3D Qubits Measured at Yale
Q = 70000*
Includes different configurations
*Bound on conventional transmon T1 : Houck et al. Phys. Rev. Lett. 101, 080502 (2008) Strong Coupling Achieved
Bare cavity Zcav g 2 F01 Dressed cavity ZZcav qubit
Cavity measurement frequency (GHz) g a 140 MHz Strong coupling g !NJ Strong Dispersive Regime g oe;2n g oe;1n g oe;0n 2F n=2 n=2 n ~0 n=1 n ~0.5 n=1
n=0 n ~1 n=0
Qubit Frequency (GHz) FJN, Strong Dispersive Hamiltonian: Stark shift per photon §· H eff Zcava a ¨¸ZVqc Fa a z now > 1,000 ©¹2 State dependent frequency shift linewidths What do we learn about Josephson junctions from 3D transmon? Quality Factor of Josephson Inductance
delay T1 = 60 Ps S f = 6.808 GHz
Q ZT1 |2,000,000 Most stringent bound on QLj t 2,000,000 the quality of Josephson Q inductance C t 2,000,000
The Josephson junction has not been limiting the SC qubit coherence Quasiparticles in Josephson Junction
Fractional quasiparticle density 2S kT x x e'/kT qp ne ' Bound for non-eq 12Z ' x Quasiparticle density qp T1 SZ = 1/Pm3 ''f xqp §·12 ¨¸ 1 f 2 ©¹SZ
T1 and frequency shift agree with theory by Catelani et al.*
One free parameter *Catelani et al. PRL 106, 077002 (2011) - gap ' PV Coherence Dominated by Non-1/f noise Conventional Ramsey transmon T*2 improved by X 10 3D T*2 = 14 Ps Ramsey with echo
Techo = 25 Ps
Exponential Ramsey envelope : Absence of 1/f noise
T*2 = 17 Ps Dephasing not yet limited by 1/f critical current noise
Reported 1/f critical current noise model** does not explain this behavior. 0
**D. J. Van Harlingen et al., Phys. Rev. B 70, 064517 (2004)
tŚĂƚ͛ƐůŝŵŝƚŝŶŐdΎ2?
T*2 is not T1 limited - source of dephasing?
Fluctuations of photons in the cavity
0 ge;0n ge;1n ge;2n The qubit dephases when the photon state changes
*A. Sears et al. in preparation (2012) tŚĂƚ͛ƐůŝŵŝƚŝŶŐdΎ2?
T*2 is not T1 limited - source of dephasing?
Fluctuations of photons in the cavity
0 ge;0n ge;1n ge;2n 1 TM ~ nN
*A. Sears et al. in preparation (2012) tŚĂƚ͛ƐůŝŵŝƚŝŶŐdΎ2?
T*2 is not T1 limited - source of dephasing?
Fluctuations of photons in the cavity
0 ge;0n ge;1n ge;2n 111 n * ¦ iNi T 22T 1TM ,int i with thermal population of photons at each n i cavity modes i. *A. Sears et al. in preparation (2012) Stability of Josephson Junction
T1 ranges from 50 Ps to 70 Ps 0
* T*2 ranges from 10 Ps to 25 Ps 0
f01 = 6 808 737 605 (608) Hz
'f ~4kHzor~0.7ppm
Frequency stable < 600 Hz : Stability in EJ or Ec - 80 ppb by introducing 3D circuit QED architecture Breakthrough in SC Qubit This work
Coherence
Number of gate operation
Charge Qubit Coherence : Saga continues
This work Number of gate operation Number of gate
No evidence found that the Josephson junction is limiting the qubit coherence Coherent control of 3D transmons
Use microwave to perform single/two qubit gates Phase Gate using Off-Resonant Cavity Driving
Zee Zeg Zge Zgg Cavity drive Cavity transmission Cavity
Frequency (2)Zc FV z a a Use a qubit state-dependent cavity coherent states
When the cavity is driven, cavity coherent state evolves giving phase to each qubit state. Phase of Driven Harmonic Oscillator
Q H(t) Apply off-resonant drive to displace the cavity I DD(T ) eiI ()T (0)
iDDH ' ()t ' ZZc d T T IDDD()T Im [*2 ]dt ' | |dt ³³00 Geometric origin Dynamical origin (Area) (energy) Single-Qubit Phase Gate (z-gate)
Two coherent states Dg and De Q corresponding to |g> and |e>
T T *2 IDDDg ()T Im g g dt 'g |g |dt ³³00 I T T *2 IDDDe ()T Im e e dt 'e |e |dt ³³00
If : Z-gate
Also single qubit geometric phase demonstrated by M. Pechal, et al. arXiv:1109.1157 (2011) Single-Qubit Phase Gate - 13.5 dBm Ramsey experiment
Msmt D gate S/2 S/2M IDvv||||22 H
- 33.5 dBm Phase is proportional No driving to the driving power. SSSSS Angle of last S/2 pulse Detuning f =60 MHz Single Qubit z-gate
No reduction in Ramsey Z-gate contrast after the gate
0 0.5 1 1.5 2 0 0.5 1 1.5 2 |D|2 |D|2 Two-Qubit Phase gate
Cavity Zee Zeg Zge Zgg drive
Dee Deg D ge D gg
Frequency
gg ge eg ee 0 o gg eiIIIIIge ge ei eg eg ei ge eg ee ee 0
If ISee : cPhase Ramsey experiments to measure two qubit phase
Applying Ramsey IIee ge gate
Ramsey Applying Ige gate
Difference in phases gives two qubit phase Iee Ramsey experiments to estimate gate fidelity
NOT Applying gate
Applying Ramsey gate
0 I ge
Comparing Ramsey contrast gives estimate on gate fidelity Demonstrating cPhase gate
IIee ge Grey is a single qubit Ramsey w/o gate
ISee Ige
IIee eg Ramsey contrast a 90%
Ieg
SSSSS Angle of last Spulse
Tgate = 200ns, ' = 80 MHz, P = 1.2 dBm Paik et al. work in progress (2012) Conclusion Demonstrated new coherence time for superconducting qubit using a new 3D cQED architecture
T1 a 60 Ps (up to 75 Ps) T2 (Ramsey) a up to 30 Ps, T2 (Echo) a up to 45 Ps
New observation of physics in Josephson junction qubits
- Josephson junction Q > 2 M (current coherence limitation in SC qubit is not the junction) - Sensitive detection of non-equilibrium quasiparticles - No evidence of 1/f noise in critical current/capacitance - Dephasing from cavity photon fluctuations.
Demonstrated single and two qubit phase gate using cavity geometric/dynamical phase in coupled 3D transmon qubits.
Paik et al. Phys. Rev. Lett. 107, 240501 (2011)