quantum coherence of josephson radio-frequency...
Post on 20-May-2020
2 Views
Preview:
TRANSCRIPT
1
QUANTUM COHERENCE OF JOSEPHSON RADIO-FREQUENCY
CIRCUITS
INTERNATIONAL SCHOOL OF PHYSICS "ENRICO FERMI"QUANTUM COHERENCE IN SOLID STATE SYSTEMS
Michel Devoret, Applied Physics, Yale University, USAand Collège de France, Paris
OUTLINE
1. Motivation: Josephson circuits and quantum information
2. Quantum-mechanical superconducting LC oscillator
3. A non-dissipative, non-linear element: the Josephson junction
4. The Cooper pair box artificial atom circuit
5. Readout of the Cooper pair box qubit
6. Coherence of Josephson circuits
7. Quantum bus concept
BREAK
2
OUTLINE
1. Motivation: Josephson circuits and quantum information
2. Quantum-mechanical superconducting LC oscillator
3. A non-dissipative, non-linear element: the Josephson junction
4. The Cooper pair box artificial atom circuit
5. Readout of the Cooper pair box qubit
6. Coherence of Josephson circuits
7. Quantum bus concept
• PHOTON
• NUCLEAR SPIN
• ION
• ATOM
• MOLECULE
• ATOMIC-SIZE DEFECT IN CRYSTAL
• QUANTUM DOT
• JOSEPHSON RF CIRCUIT
IMPLEMENTATIONS OF A SINGLE, MANIPULABLE, QUANTUM-MECHANICALLY
COHERENT SYSTEM
micro
MACRO
couplingwith envt.
(Leggett, '80)
3
CLASSICAL RADIO-FREQUENCY CIRCUITS
Hergé, Moulinsart
1940's : MHz 2000's : GHz
Communication
Computation
US Army Photo
Communications
Sony
WHAT IS A RADIO-FREQUENCY CIRCUIT? A RF CIRCUIT IS A NETWORK OF ELECTRICAL ELEMENTS
element
node p
loopbranch
np
node n
Vnp
Inp
TWO COLLECTIVE DYNAMICAL VARIABLES CHARACTERIZETHE STATE OF EACH DIPOLE ELEMENT AT EVERY INSTANT:
Voltage across the element:
Current through the element:
( )p
nnpV t E d= ⋅∫( ) nnp pj dI t σ= ⋅∫∫
4
EACH ELEMENT IS TAKEN FROM A FINITE SET OF ELEMENT TYPES
inductance:
capacitance:
V = L dI/dt
I = C dV/dt
resistance: V = R IIds = G(Igs,Vds,) VdsIgs = 0
transistor: g
s d
diode: I=G(V)
CONSTITUTIVE RELATIONS
EACH ELEMENT TYPE IS CHARACTERIZED BY A RELATION BETWEENVOLTAGE AND CURRENT
LINEAR NON-LINEAR
QUANTUM INFORMATION ECONOMY
suppose a function f { } ( ) { }0,1023 0,1023j k f j∈ → = ∈
Classically, need 1000 ×10-bit registers (10,000 bits) to storeinformation about this function and to work on it.
Quantum-mechanically, a 20-qubit register can suffice!
( )2 1
/ 20
12
N
Nj
j f j−
=
Ψ = ∑
Function encoded in a single quantum state of small register!(but a highly entangled one)
10 q-bits 10 q-bits
5
CAN WE BUILD A COMPLETE SET OF QUANTUM INFORMATION PROCESSING PRIMITIVES
OUT OF SIMPLE CIRCUITSTHAT WE WOULD CONNECT TO PERFORM ANY
DESIRED FUNCTION?
QUESTION:
TRANSM. LINES, WIRES
COUPLERS
CAPACITORS
GENERATORS
AMPLIFIERS
JOSEPHSON JUNCTIONS
FIBERS, BEAMS
BEAM-SPLITTERS
MIRRORS
LASERS
PHOTODETECTORS
ATOMS
DRAWBACKS OF CIRCUITS:
ADVANTAGES OF CIRCUITS: - PARALLEL FABRICATION METHODS- LEGO BLOCK CONSTRUCTION OF HAMILTONIAN- ARBITRARILY LARGE ATOM-FIELD COUPLING
ARTIFICIAL ATOMS PRONE TO VARIATIONS
QUANTUM OPTICS QUANTUM RF CIRCUITS
~
6
OUTLINE
1. Motivation: Josephson circuits and quantum information
2. Quantum-mechanical superconducting LC oscillator
3. A non-dissipative, non-linear element: the Josephson junction
4. The Cooper pair box artificial atom circuit
5. Readout of the Cooper pair box qubit
6. Coherence of Josephson circuits
7. Quantum bus concept
SIMPLEST EXAMPLE: SUPERCONDUCTING LC OSCILLATOR CIRCUIT
A CIRCUIT BEHAVING QUANTUM-MECHANICALLYAT THE LEVEL OF CURRENTS AND VOLTAGES ?
d ~ 0.5 mm
7
MICROFABRICATION L ~ 3nH, C ~ 1pF, ωr /2π ~ 5GHz
SIMPLEST EXAMPLE: SUPERCONDUCTING LC OSCILLATOR CIRCUIT
A CIRCUIT BEHAVING QUANTUM-MECHANICALLYAT THE LEVEL OF CURRENTS AND VOLTAGES ?
d ~ 0.5 mm
d << λ: LUMPED ELEMENT REGIME
MICROFABRICATION L ~ 3nH, C ~ 1pF, ωr /2π ~ 5GHz
SIMPLEST EXAMPLE: SUPERCONDUCTING LC OSCILLATOR CIRCUIT
A CIRCUIT BEHAVING QUANTUM-MECHANICALLYAT THE LEVEL OF CURRENTS AND VOLTAGES ?
INCOMPRESSIBLE ELECTRONIC FLUID SLOSHES BETWEEN PLATES.NO INTERNAL DEGREES OF FREEDOM.
d ~ 0.5 mm
d << λ: LUMPED ELEMENT REGIME
SUPERCONDUCTIVITY ONLY ONE COLLECTIVE VARIABLE
8
Rydberg atom SuperconductingLC oscillator
L C
DEGREE OF FREEDOM IN ATOM vs CIRCUIT:SEMI-CLASSICAL DESCRIPTION
Rydberg atom SuperconductingLC oscillator
L C
velocity of electron → voltage across capacitorforce on electron → current through inductor
DEGREE OF FREEDOM IN ATOM vs CIRCUIT:SEMI-CLASSICAL DESCRIPTION
2 Possible correspondences: velocity of electron → current through inductor force on electron → voltage across capacitor
charge dynamics
field dynamics
9
Rydberg atom SuperconductingLC oscillator
velocity of electron → voltage across capacitorforce on electron → current through inductor
DEGREE OF FREEDOM IN ATOM vs CIRCUIT
2 Possible correspondences: velocity of electron → current through inductor force on electron → voltage across capacitor
charge dynamics
field dynamics
φL C
semiclassical picture
+Qφ
-Q
FLUX AND CHARGE IN LC OSCILLATOR
LIφ = Q VC=
V
-I
X
Mk
electrical world mechanical world
I
f
position variable: φ X-Xeqmomentum variable: Q Pgeneralized force : Ι fgeneralized velocity: V V
1eqX X
kf=− P VM=
generalized mass : C Mgeneralized spring constant: 1/L k
10
+Qφ
-Q
HAMILTONIAN FORMALISM
V
X
Mk
electrical world mechanical world
I
f
( ) ( )22
,2 2
eqQH QC L
φ φφ
−= +
charge on capacitor
time-integralof voltage oncapacitor
conjugate variables
( ) ( )22
,2 2
eqk X XPH X PM
−= +
momentum of mass
positionof massw/r wall
conjugate variables
+Qφ
-Q
HAMILTON'S EQUATION OF MOTION
V
X
Mk
electrical world mechanical world
I
f
H QQ C
HQL
φ
δφφ
∂= =
∂∂
= − =∂
H PXP MHP k XX
δ
∂= =
∂∂
= − =∂
1r LC
ω = rkM
ω =
11
FROM CLASSICAL TO QUANTUM PHYSICS:CORRESPONDENCE PRINCIPLE
ˆ
ˆX X
P P
→
→
( ) ( )ˆ ˆ ˆ, ,H X P H X P→
position operator
momentum operator
hamiltonian operator
{ } ˆ ˆ, , /PB
A B A B A B A B iX P P X
∂ ∂ ∂ ∂ ⎡ ⎤− = → ⎣ ⎦∂ ∂ ∂ ∂Poisson bracket
commutator
{ } ˆ ˆ, 1 ,PB
X P X P i⎡ ⎤= → =⎣ ⎦position andmomentumoperators donot commute
+Qφ
-Q
FLUX AND CHARGE DO NOT COMMUTE
V
I
ˆ ˆ, iQφ⎡ ⎤⎣ =⎦
We have obtained this resultthru correspondance principleafter having recognized fluxand charge as canonical conjugatecoordinates.
"Cannot quantize the equations of the stock market!"A.J. Leggett
We can also obtain this result from quantum field theory thru the commutationrelations of the electric and magnetic field. Tedious.
For every branch in the circuit:
12
+Qφ
-Q
φ
E
LC CIRCUIT AS QUANTUMHARMONIC OSCILLATOR
rωh
( )†
†
ˆ 1ˆ ˆ 2ˆ ˆ ˆ ˆ
ˆ ˆ;
2
2
r
r r r r
r r
r r
H a a
Q Qa i a iQ Q
L
Q C
ω
φ φφ φ
φ ω
ω
= +
= + = −
=
=
annihilation and creation operators
0
φ
φ
SUPPRESSION OF THERMAL EXCITATIONOF LC CIRCUIT
Br k Tω5 GHz 10mK
rωhI
E
Can place the circuitin its ground state
13
φ
φ
WAVEFUNCTIONS OF LC CIRCUIT
rωhI
φ
E
Ψ(φ)Ψ0
0Ψ1
In every energy eigenstate,(photon state)
current flows in opposite directions simultaneously!
2 rφ
φ
φ
EFFECT OF DAMPING
important:as little dissipation
as possibledissipation broadens energy levels
E
112 2n r
r
iE n
RC
ω
ω
⎡ ⎤⎛ ⎞= + +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦=
seemorelater
14
φ
φ
E
ALL TRANSITIONS ARE DEGENERATE
CANNOT STEER THE SYSTEM TO AN ARBITRARY STATEIF PERFECTLY LINEAR
rωh
Potential energy
Position coordinate
NEED NON-LINEARITY TO FULLYREVEAL QUANTUM MECHANICS
15
OUTLINE
1. Motivation: Josephson circuits and quantum information
2. Quantum-mechanical superconducting LC oscillator
3. A non-dissipative, non-linear element: the Josephson junction
4. The Cooper pair box artificial atom circuit
5. Readout of the Cooper pair box qubit
6. Coherence of Josephson circuits
7. Quantum bus concept
JOSEPHSON JUNCTIONPROVIDES A NON-LINEAR INDUCTOR
1nm SI
S
superconductor-insulator-
superconductortunnel junction
CjLJ
16
JOSEPHSON JUNCTIONPROVIDES A NON-LINEAR INDUCTOR
1nm SI
S
superconductor-insulator-
superconductortunnel junction
CjLJ
Ι
( )' 't
V t dtφ−∞
= ∫
JOSEPHSON JUNCTIONPROVIDES A NON-LINEAR INDUCTOR
1nm SI
S
superconductor-insulator-
superconductortunnel junction
φ
ΙΙ = φ / LJ
( )0 0sin /I I φ φ=
CjLJ
Ι
( )' 't
V t dtφ−∞
= ∫
0 2eφ =
20 0
0J
J
LE Iφ φ
= =
17
COUPLING PARAMETERSOF THE JOSEPHSON JUNCTION "ATOM"
THE hamiltonian:(we mean it!)
( )ˆ ' 't
V t dtφ−∞
= ∫REST
OFCIRCUIT
extq
( )21 2cos2 ext
jJj
CH EQ q eφ
= − −
I
( )ˆ ' 't
Q I t dt−∞
= ∫
2
0
212 ˆ
ˆ 14e
erm
AH epπε
⎛ ⎞= − −⎜ ⎟⎝ ⎠
RESTOF
CIRCUIT
extq
THE hamiltonian:(we mean it!)
( )21 2cos2 ext
jJj
CH EQ q eφ
= − −
COUPLING PARAMETERSOF THE JOSEPHSON JUNCTION "ATOM"
Comparable with lowest ordermodel for hydrogen atom
18
TWO ENERGY SCALESTwo dimensionlessvariables:
ˆˆ
ˆˆ
2
2QN
e
e
φϕ =
=
ˆˆ, iNϕ⎡ ⎤ =⎣ ⎦
( )2
co8 ˆs2
ext
JCj
NE EH
Nϕ
−= −
2
2Cj
E eC
=
2x
exte tqNe
=
Hamiltonian becomes :
Coulomb charging energy for 1e
18JE = ΔNT
Josephson energy
gap
# condion channels
barrier transpcy
reduced offset charge
valid foropaque barrier
LOW-LYING EXCITATIONS OF ISOLATEDJUNCTION: CHARGE STATES
____
++++
-ne+ne
0 2 4-2-4n = N/2 = 6
2Δ
e tunnelingCP tunneling
4 CE
JE
19
MECHANICAL ANALOG OF JOSEPHSONCOUPLING ENERGY
rotatingmagnet
angular velocity:4 C
extE NΩ =h
compass needle
needleangular momentum:
Nh
torque on needle due to magnetvelocity of needle in magnet frame
current through junctionvoltage across junction
ϕ̂
CHARGE STATES vs PHOTON STATES
ϕ
N A1
A2n
θ
Hilbert spaces have different topologies
20
HARMONIC APPROXIMATION
( )2
co8 ˆs2
ext
JCj
NE EH
Nϕ
−= −
( )22
,2ˆ
82
e
Cj h J
xtNE
NEH ϕ−
= +
8 CP
JE Eω =Josephson plasma frequency
Spectrum independent of DC value of Next
TUNNEL JUNCTIONSIN REAL LIFE
100nm
EJ ~ 50K
EJ ~ 0.5K
ωp ~ 30-40GHz
credit L. Frunzio and D. Schuster
credit I. Siddiqi and F.Pierre
21
OUTLINE
1. Motivation: Josephson circuits and quantum information
2. Quantum-mechanical superconducting LC oscillator
3. A non-dissipative, non-linear element: the Josephson junction
4. The Cooper pair box artificial atom circuit
5. Readout of the Cooper pair box qubit
6. Coherence of Josephson circuits
7. Quantum bus concept
3 TYPES OF BIASES
I0
C
U
2Cg2Cg
I0
C
Ib
I0
C ΦbL
charge flux current
22
EFFECTIVE POTENTIALOF 3 BIAS SCHEMES
-1 +1 phase bias
flux bias
charge bias
UC Berkeley, NIST, UCSB,U. Maryland, CRTBT Grenoble...
TU Delft, NEC, NTT, MITUC Berkeley, IBM, SUNYIPHT Jena ....
CEA Saclay, YaleNEC, Chalmers, JPL, ...
22
eh
ϕπ
φ=
2ehφ
2ehφ
EFFECTIVE POTENTIALOF 3 BIAS SCHEMES
-1 +1 phase bias
flux bias
charge bias
UC Berkeley, NIST, UCSB,U. Maryland, CRTBT Grenoble...
TU Delft, NEC, NTT, MITUC Berkeley, IBM, SUNYIPHT Jena ....
CEA Saclay, YaleNEC, Chalmers, JPL, ...
2ehφ
2ehφ
2ehφ
23
U
Φ
island
COOPER PAIR"BOX"
Bouchiat et al. 97Nakamura, Pashkin & Tsai 99Vion et al. 2002
2 control parameters CgU/2e and Φ/Φ0
U
ΦCg
ANHARMONICITY vs CHARGE SENSITIVITY
Cooper pair box soluble in terms of Mathieu functions (A. Cottet, PhD thesis, Orsay, 2002)
24
290 μm
ANHARMONICITY vs CHARGE SENSITIVITYIN THE LIMIT EC/EJ << 1 ("TRANSMON")
peak-to-peak charge modulation amplitude of level m:
anharmonicity:
TRANSMON: SHUNT JUNCTION WITH CAPACITANCE
Courtesy of J. Schreier and R. Schoelkopf
J. Koch et al. 07
( )12 01
12 01 / 2 8C
J
EE
ω ωω ω
−→
+
ω01
ω12ω02 2
Sufficient to control the junction as a two level system
SPECTROSCOPY OF A COOPER PAIR BOXIN TRANSMON REGIME
Anharmonicity: 01 12 455MHz CEω ω− =
ω01
ω02 2
ω12J. Schreier et al. 07
Slide courtesy of J. Schreier and R. Schoelkopf
T1 > 2μs
25
ATOM IN SEMI-CLASSICAL REGIME:CIRCULAR RYDBERG ATOM
p+
2 nr
nω
2
20
2
1 3
1
Ry
Ry2
2
e
n
n
n n
nn n
m r n
r a n
En
nerd
ω
ω → ±
→ ±
=
=
= −
=
=Coulombpotential
old Bohr theory essentially “exact”!
constraint
valid when: ( ) 1EE
ω∂∂
( )2
, ,n x y zΨ
Josephsonpotential energy
Junction phase ϕ
TRANSMON AS ANALOG OF CIRCULARRYDBERG ATOMS
2EJ
ω
Spectroscopic lines (high T):
+π−π
0
01ω12ω , 1 1, 2 , 1n n n n n nω ω ω+ + + +−
26
Josephsonpotential energy
Junction phase ϕ
TRANSMON AS ANALOG OF CIRCULARRYDBERG ATOMS
2EJ
ω
Spectroscopic lines (low T):
+π−π
OUTLINE
1. Motivation: Josephson circuits and quantum information
2. Quantum-mechanical superconducting LC oscillator
3. A non-dissipative, non-linear element: the Josephson junction
4. The Cooper pair box artificial atom circuit
5. Readout of the Cooper pair box qubit
6. Coherence of Josephson circuits
7. Quantum bus concept
27
THE READOUT PROBLEM
QUBIT READOUTON
OFF0 1
10 or
THE READOUT PROBLEM
QUBIT READOUTON
OFF0 1
QUBIT READOUTON
OFF0 1 QUBIT READOUT
ON
OFF
1) SWITCH WITH LARGE ON-OFF RATIO2) FAITHFUL READOUT CIRCUITWANT:
0 1
10
28
DIVERSITY OF CIRCUIT STRATEGIES
YALE (circuit-QED)analogous to cavity QED expts by
Haroche, Raimond, Brune et al.
SACLAY -- YALE (Quantronium) TU DELFT -- NEC -- NTT
NIST -- UCSB
QUBITCHIP
DISPERSIVE READOUT STRATEGY
10 or
rf signal in
01ω ω≠
29
QUBITCHIP
or
10 or
QUBIT STATEENCODED IN PHASE
OF OUTGOING SIGNAL,NO ENERGY DISSIPATED
ON-CHIP
rf signal in rf signal out
DISPERSIVE READOUT STRATEGY
QUBITCHIP
10
or
or
rf signal in rf signal out
DO WITH ENOUGH PHOTONS TO GET1 CLASSICAL BIT OF INFORMATION
DISPERSIVE READOUT STRATEGY
Requirements: 1) low noise in detection2) enough phase shift
30
QUBITCHIP
10
or
or
rf signal in rf signal out
DO WITH ENOUGH PHOTONS TO GET1 CLASSICAL BIT OF INFORMATION
DISPERSIVE READOUT STRATEGY
Requirements: 1) low noise in detection2) enough phase shift
PLACE QUBIT IN MICROWAVE CAVITYTO FILTER OUT IRRELEVANT PART OF SPECTRUM
Si or Al2O3
Al or Nb
SUPERCONDUCTING MICROWAVE RESONATOR: ANALOG OF FABRY-PEROT CAVITY
can get Qup to 106
( in bulk:Q ~ 1010)
length ~1cm, but photon propagation length ~ 10km!
mirror = capacitors
COPLANAR WAVEGUIDE: 2D VERSION OF COAXIAL CABLE
31
Si or Al2O3
Al or Nb
SUPERCONDUCTING MICROWAVE RESONATOR: ANALOG OF FABRY-PEROT CAVITY
~
can get Qup to 106
( in bulk:Q ~ 1010)
ADC
IN OUT
CHIP
length ~1cm, but photon propagation length ~ 10km!RFGEN.
Si or Al2O3
Al or Nb
SUPERCONDUCTING MICROWAVE RESONATOR: ANALOG OF FABRY-PEROT CAVITY
~
can get Qup to 106
( in bulk:Q ~ 1010)
ADC
length ~ 1cm, but photon decay length ~ 10km!
IN OUT
1/2 photon: ~1nA~100nV
ν ~ 10GHz
CHIP
w~20μm
VERY SMALL MODE VOLUME
32
3mm
10mm
100μm
Nb
SUPERCONDUCTING CAVITY = FABRY-PEROT
qubit goes here
10µm
CPW ground
CPW ground
ISLAND
READOUT JUNCTION
"QUANTRONIUM" IN MICROWAVE CAVITY
33
10-20 mK2-20 GHz
HIGH FREQUENCIES, LOW TEMPERATURES
OFF-RESONANT NMR-TYPEPULSE SEQUENCE
FOR QUBIT MANIPULATION
QUANTRONIUM IN MICROWAVE CAVITY
34
|0>
|1>
READOUTPROBING
PULSE
QUBIT STATEENCODED IN PHASE
OF TRANSMITTED PULSE
or
QUANTRONIUM IN MICROWAVE CAVITY
|0>
|1>
QUANTRONIUM IN MICROWAVE CAVITY
~ ADCIN OUT
AWG
40ns40ns200ns
t t
Metcalfe et al.Phys. Rev. B6174516 (2007)
35
|0>
|1>
QUANTRONIUM IN MICROWAVE CAVITY
~ ADCIN OUT
AWG
40ns40ns200ns
t t
Metcalfe et al.Phys. Rev. B6174516 (2007)
latching effectdue to bifurcation
of cavity mode
CAVITY BIFURCATION : ANALOG OF OPTICALBISTABILITY
36
HYSTERESIS
0
1
Ω/2π = 4.2GHzT=15mK
1 ms sweep
Urf
MEASUREMENT OFREADOUT FIDELITY
Slope3 timestoo smallcomparedwith thy
Relaxationinduced byreadout
π pulse Urf
TOO MANY READOUT PHOTONS?
37
JOSEPHSONPARAMETRIC
AMPLIFIERSIGNAL
IDLER
180ºhybrid
coupler
Design goals:TN < hf/kBGain > 20 dBBandwidth > 5 MHzDynamic range > 20 dB chip
Φ0/2Josephson ringmodulator
Bergeal et al. 08
OUTLINE
1. Motivation: Josephson circuits and quantum information
2. Quantum-mechanical superconducting LC oscillator
3. A non-dissipative, non-linear element: the Josephson junction
4. The Cooper pair box artificial atom circuit
5. Readout of the Cooper pair box qubit
6. Coherence of Josephson circuits
7. Quantum bus concept
38
CAVITY QUANTRONIUMRABI OSCILLATIONS
M. Metcalfe et al.
0
1
νLarmor=14.5GHz
20%
40%
60%
acqu
isiti
on ti
me
(s)
RAMSEYFRINGES
T2 =500ns+-
200ns
0
1
39
Lopsided frequency fluctuations
Charge noise amplitude1/f2
3( ) , 1.9 10gNS eαω α
ω−= ∼
value OKEJ/EC = 3.6
(Karlsruhe)
method A of van Harlingen et al. 2004
DISTRIBUTION OF RAMSEY DATA
Need larger EJ/EC
Lopsided frequency fluctuations
Charge noise amplitude1/f2
3( ) , 1.9 10gNS eαω α
ω−=
value OK
DISTRIBUTION OF RAMSEY DATA
(Karlsruhe)
van Harlingen et al. 2004
40
DECOHERENCE TIME ( T2 )
Δt (ns)
Δt
Qφ = ωLarmorT2
'02 Vion et al. 50,000'05 Siddiqi et al. 30,000'05 Wallraff et al. 19,000'06 Metcalfe et al. 70,000'08 Houck et al. 100,000
1 param. fit→ T2 = 300ns
νLarmor=18.984GHz
Siddiqi et al, 06
phase
flux
charge
ΔECΔEJΔQoffbias
junction noises
SENSITIVITY OF BIAS SCHEMES TO NOISE (EXPD)
chargequbit
fluxqubit
phasequbit
- +-
CHARGED IMPURITYTUNNEL CHANNEL
ELECTRIC DIPOLES
41
OUTLINE
1. Motivation: Josephson circuits and quantum information
2. Quantum-mechanical superconducting LC oscillator
3. A non-dissipative, non-linear element: the Josephson junction
4. The Cooper pair box artificial atom circuit
5. Readout of the Cooper pair box qubit
6. Coherence of Josephson circuits
7. Quantum bus concept
QUANTUM BUS CONCEPT FOR SOLID STATE QUBITS
Nature, 27 Sept. 2007
artificial atom
microwave transmission line resonator
coupling element
42
2g = 250 MHz!
cavityqubit
Msmt. of qubit-cavity avoided crossing vacuum Rabi splitting
STRONG QUBIT-CAVITY COUPLING
~ ADCIN OUT
~
CPB
RESOLVING PHOTONNUMBER IN CAVITY
( )( )!
nnnP n e
n−=
• Mean shifts
• Peaks are Poisson distributed
• Peaks get broader n∝
Houck et al., Nature 07
43
RESOLVING PHOTONNUMBER IN CAVITY
CONDITIONAL QUBITROTATION POSSIBLE!
Blais A. et al., Phys. Rev. A 75, 032329 2007
SCHEMATIC OF 2 COOPER PAIR BOXESIN A MICROWAVE CAVITY
44
SWAPPING INFORMATION BETWEEN QUBITS
Background due to
off-resonant driving by the
Stark tone
Nota Bene:(Using first generationtransmon with ‘short’
T2=100 ns.)
J. Majer, J. M. Chow et al, Nature, 449, 443 (2007)Similar results with phase qubits: Sillanpaa et al, Nature, 449, 438 (2007)
QUANTUM COMPUTATIONviolation of Bell's inequalities teleportationerror correctionalgorithms
MEASUREMENTS AND CONTROL OF QUANTUM ENGINEERED SYSTEMS
amplification at the quantum limitquantum noise squeezing (1-mode and 2-mode)quantum feedbacksingle photon detection for radioastronomycharge counting for metrology
PERSPECTIVES
Qφ ~ 107
NEWMATERIALS?
Qφ ~ 104
OK
45
Circuit Quantum Electrodynamics GroupsDepts. Applied Physics and Physics, Yale
P.I.'sGrads
Post-Docs
Res. Sc.
UndrgrdsCollab.
M. D.R. VIJAYC. RIGETTIM. METCALFEV. MANUCHARIANI. SIDDIQI (UCB)E. BOAKNIN (Mtrl)N. BERGEALP. HYAFIL
S. FISSETTED. ESTEVE(Saclay)
S. GIRVINT. YUL. BISHOP
J. KOCHJ. GAMBETTA
F. MARQUARDT(Munich)A. BLAIS(Sherbrooke)
A. CLERK (McGill)
R. SCHOELKOPFJ. CHOWB. TUREKJ. SCHREIERB. JOHNSONA. WALRAFF (ETH)H. MAJER (Vienna)A. HOUCKD. SCHUSTERL. FRUNZIOJ. SCHWEDEP. ZOLLER(Innsbruck)
top related