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Alexey Ustinov Two-level fluctuators in Josephson junctions
Josephson junction as a tool to manipulate microscopic two-level systemsJ. Lisenfeld, P. Bushev, A. Lukashenko
C. Müller, A. Shnirman, J. H. Cole, A. V. Ustinov
Universität Karlsruhe, Germany
10
2 nmAlOX
Al
Al
I.F. Schegolev Memorial Conference “Low-Dimensional Metallic and Superconducting Systems”
October 11-16, 2009 - Chernogolovka
Alexey Ustinov Two-level fluctuators in Josephson junctions
Outline
JJ phase qubitMicrowave spectroscopyTwo-level fluctuators (TLFs)Manipulating a TLF by the qubitDirect driving of TLFs by microwavesEntangling two or more TLFs
J. Lisenfeld, C. Mueller, J. H. Cole, A. Lukashenko, A. Shnirman, and A. V. Ustinov. ArXiv:0909.3425
Alexey Ustinov Two-level fluctuators in Josephson junctions
Josephson tunnel junction
electricalfield
-+ - +
Nb or Al
AlOX
Nb or Al
equivalent circuit
-
+
two-level fluctuator (TLF)
electrical dipole
Alexey Ustinov Two-level fluctuators in Josephson junctions
Spectroscopic evidences of two-level fluctuators (TLFs)
-
+
two-level fluctuator (TLF)
electrical dipole
10
2 nmAlOX
Al
Al mic
row
ave
frequ
ency
, G
Hz
external flux cext / ΦΦ
45 MHz
201 eg +
201 eg −
g1
e0
microscopictwo-level fluctuators
e0
swapping a photon from qubit to TLF
Pesc
g1
Alexey Ustinov Two-level fluctuators in Josephson junctions
Phase qubit readout: Tunneling from the excited state
ener
gy
phase
0
1
ϕ
Readout by applying a tilt (current) pulse
tunneling rate
0Γ
03
1 10 Γ⋅≈Γ
current
time
tunneling event
I
current
Alexey Ustinov Two-level fluctuators in Josephson junctions
Reducing dissipation by placing the junction in a loop
ϕ0 2π 4π
ener
gy
U(ϕ
)
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
Φ= ϕϕ
πϕ cos
2)( 0
c
c
IIIU
L Ren
ergy
U
(ϕ)
ϕ0 2π
I
current current
0
1
⎥⎥⎦
⎤
⎢⎢⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛ΦΦ
−Φ
= ϕπϕβπ
ϕ cos221
2)(
2
0
0
L
cIU
Φ
01
85.00
≈ΦΦ
Alexey Ustinov Two-level fluctuators in Josephson junctions
Josephson phase qubit
readout SQUID qubit loop
fluxline
microwave line
1 μmqubit junction J. Lisenfeld et al.,
Phys. Rev. Lett. 99, 170504 (2007)
Alexey Ustinov Two-level fluctuators in Josephson junctions
Origin of decoherence in phase qubits: microscopic two-level fluctuators
AS 1
max ∝
spectroscopy
S
K. B. Cooper, et al., Phys.Rev.Lett. 93, 180401 (2004).
A is the junction area
Alexey Ustinov Two-level fluctuators in Josephson junctions
exponential fit
Josephson junction as a quantum system - an artificial ‘atom’
01ωh
I
current
ener
gy
phase
Rω
2
ϕ
01ω Rω
analog of a two-level atom
0
1
1
0
Alexey Ustinov Two-level fluctuators in Josephson junctions
Swapping a quantum state of qubit with the state of two-level fluctuator
Δt
external flux cext / ΦΦ
40 MHz
Pes
c
Δt
time for SWAP gate: 23ns(half period of coupled osc.)
Pe
scg1
e0
g1
e0
g1
2MHz22
2vac S
≈=π
ω
Δt
mic
row
ave
frequ
ency
, G
Hz
Alexey Ustinov Two-level fluctuators in Josephson junctions11
ns850T TLF,1 ≈
see also:M. Neeley, M. Ansmann, J. Martinis, et. al.,Nature Physics 4, 523 (2008)
ss,s, n210T2.1Tn400T TLF,2TLF,1Qubit,1 ≈≈≈ μ
ns110T Qubit,1 ≈
Using a two-level fluctuator as a quantum memory
Alexey Ustinov Two-level fluctuators in Josephson junctions
an excited multi-level system could absorb additional photons
Is TLF really a two-level system ? Yes, it is.
Outcome: no oscillations when both TLF and qubit arein their excited states and coupled
Alexey Ustinov Two-level fluctuators in Josephson junctions
time domain data frequency domain data
Rabi oscillations of the qubit in the vicinity of a TLF: Data
Sweeping flux through splitting, at each flux adjusting microwave frequency to qubit resonance and recording a Rabi oscillation trace.
Alexey Ustinov Two-level fluctuators in Josephson junctions
xxzzqs SH τστεσε 21
f21
21 +−−=emHHHH Is ++=
( ) ( )−+
+−+
+ +Ω++Ω= ττσσ aaaaH qI f21
21( )2
1em += +aaH dωh
qubit TLF qubit-TLF coupling
field:
Hamiltonian:
qubit-field coupling TLF-field coupling
symmetric0f =Ω
Transitions in the driven 4-level system: qubit coupled to TLF
not symmetric1.0f =Ω
Theory: C. Müller, J. H. Cole, andA. Shnirman (Karlsruhe)
Alexey Ustinov Two-level fluctuators in Josephson junctions
Theory: C. MüllerJ. H. ColeA. Shnirman(Karlsruhe)
Rabi oscillations of the qubit in the vicinity of TLF: Comparison in time domain
experiment theory
Alexey Ustinov Two-level fluctuators in Josephson junctions
Dipole size fit from theory:
nm12.0d06.0 ≈≈p
nm2d ≈with dielectric thickness
Asymmetric pictureindicates direct coupling of TLF todriving field
experiment theory
Rabi oscillations of the qubit in the vicinity of TLF: Comparison in frequency domain
Alexey Ustinov Two-level fluctuators in Josephson junctions17
Direct excitation of a TLF by applying microwaves
Rabi oscillations in TLF
Alexey Ustinov Two-level fluctuators in Josephson junctions18
220, Δ+= =ΔRR ωω
220
20
Δ+=
AAA
Rabi oscillations in a directly driven TLF : Dependence on driving field detuning
Alexey Ustinov Two-level fluctuators in Josephson junctions19
Ramsey oscillations in a directly driven two-level fluctuator: Dephasing time T2
Alexey Ustinov Two-level fluctuators in Josephson junctions20
Two-level fluctuator has much longer T1 time than the JJ qubit
Rabi oscillations of TLF
Rabi oscillations of the qubit
TLF is a better qubit than JJ ...
Alexey Ustinov Two-level fluctuators in Josephson junctions21
Rabi oscillation in TLF versus qubit ‘parking’ position
microwave field strength ‘seen’ by TLF depends on the qubit resonance frequency
qubit ‘parking’
Alexey Ustinov Two-level fluctuators in Josephson junctions
Migration of fluctuators due to thermal annealing
Center: 7.82 GHzMagnitude: 24 MHz
Center: 7.65 GHzMagnitude: 24 MHz
Data taken on 18.02.09after annealing at 1.8 Kfor a few hours
Data taken on 12.02.09
Alexey Ustinov Two-level fluctuators in Josephson junctions23
ns50ns129ns150
2
1
≈≈≈
TTTd
MHz25GHz656.710
==
Sf
ns110ns715ns600
2
1
≈≈≈
TTTd
MHz21GHz845.710
==
Sf
ns300~ns150ns250
2
1
TTTd
≈≈
MHz21GHz021.810
==
Sf
Possibility to entangle two or more TLFs
magnetic flux (arb. units)
Data taken after annealing at 400 mKfor several minutes
Alexey Ustinov Two-level fluctuators in Josephson junctions
Conclusions
TLFs may have longer coherence times than qubits
they can be used as a built-in quantum memorythey allow to entangle a macroscopic object with microscopic defect and study a coupled quantum system
TLFs show direct coupling to the electrical ac field in the junction
they can be directly controlled by microwavesa qubit is only necessary to measure them
Full quantum control and characterization of individual TLFs is readily possible
10
2 nmAlOX
Al
Al
Alexey Ustinov Two-level fluctuators in Josephson junctions
Thanks to my collaborators
J. Lisenfeld, P. Bushev, A. Lukashenko (experiment)C. Müller, J. H. Cole, A. Shnirman (Karlsruhe, theory) J. M. Martinis, M. Ansmann (UCSB, sample fab)
Karlsruhe experimental team
J. Lisenfeld, C. Mueller, J. H. Cole, A. Lukashenko, A. Shnirman, and A. V. Ustinov. ArXiv:0909.3425
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