Interfacing quantum optical and solid state qubits Cambridge, Sept 2004 Lin Tian Universität Innsbruck Motivation: ion trap quantum computing; future roads.
Post on 23-Dec-2015
216 Views
Preview:
Transcript
Interfacing quantum optical and solid state qubits Cambridge, Sept 2004
Lin Tian
Universität Innsbruck
• Motivation: ion trap quantum computing; future roads for exploring • Interfacing with solid-state devices: protocols -- hybrid qubit & quantum trap; realization -- superconducting qubit• Other approaches -- …
References:Tian, Rabl, Blatt & Zoller, PRL (’04)
Innsbruck People :R. Blatt (experiment) P. RablL. TianI. Wilson-RaePeter Zoller
In collaboration with :A. Imamoglu (ETH)I. Martin (LANL)A. Shnirman (Karlsruhe)
Ion Trap -- charged particles in electromagnetic potential
• Harmonic confinement, laser manipulation
Hs p x2
2m 1
2m
2x2 0
2 z
s Rt2
s eik lx h. c.
n,g|
n,e| 1n,e|
1n,e|
1n,g|
1n,g|
a
a
red side band -- blue side band0 : detuning= k x <
Generate various Hamiltonian• e.g J-C type of model
Applications• laser cooling by optical pumping• quantum state engineering• precision measurement• quantum computing …
D. Leibfried et al, RMP (2003)
Motional degreeInternal degree
Ion Trap Quantum ComputingIon Trap Quantum Computing
Cirac and Zoller (’95).
j1i
j0i
• Internal state of trapped ion as qubits• Center of mass motion as media• Swap states of spin and motion
|g, 0n |e, 0n |g, 0n |g, 1n
Hint R
2
s â s â
Progress in the past 10 years : experiment: CNOT, teleportation, small algorithm, entanglement, (Innsbruck, NIST, Michigan…)
theory: fast gate, quantum phase transition with ions,topological gate, scalability …
Scalable Ion Trap Schemes by Moving Ions
-- Kielpinski, Monroe, Wineland (02)
¹x2(t)
d¹x1(t)
Hint z1 z
2
Segmented trap Moving head-- Cirac, Zoller (00)
Scalable ion trap quantum computingwithout moving ions over long distance?
Progress and problems of quantum optical system in quantuminformation processing?• Ion trap experiments• Optical lattices • Atomic and photonic states entanglement• Efficiency and Scalability• Decoherence
Connecting with solid-state systems ??
• Advantages ?? (what do we gain ?)• Difficulties ?? (decoherence, compatibility, coupling, scalability)• Can we integrate the best of both, any limit for improving the experiments?
quantuminformation
mesoscopicelectronicsquantum
optical
ion trap quantum computing by connecting with solid-state devices
ion trap quantum computing by connecting with solid-state devices
hybrid qubit approach: Ion trap qubit as storage Solid-state charge qubit as processor Capacitive coupling between the two
snsjs2s1
qnqjq2q1
qi qj
Technical Difficulties: ion trap vs charge qubit• laser of trap affects with charge qubits• ion trap at low temperature, …
quantum trap approach: coupling between ion and trap mode trap mode is quantum effective interaction between ions
Realization -- with superconducting devices
• Coupling with the motion of trapped ions• Hybrid qubit – superconducting charge qubit, double dot qubit• Quantum trap – EM modes in superconducting cavity
• Exchange information between ion qubit and charge qubit• Decoherence• Scalability
Spin-dependent interaction induced by laser pulses -- mechanism
| |
R
| |
polarized laser pulse |, |, |0i
ion interaction with charge: dipole – charge| |
R1
R2
Q
|, |,
R 0 -- initial distance
Hint tx zq .HdQ Qe|R1 R2 |
4 0R02 z
s zq
dR
ion interaction with ion: dipole -- dipole
| |
|, |, | |
|, |,
R 0
Hd d e2dR2
4 0R03
z1s z2
s
Superconducting QubitsSuperconducting Qubits
Charging Energy Josephson Energy
Uc C2
0
2ddt
2UJ 0I c
2 1 cos
Ec e2
2CEJ 0I c
2
Charge Qubits EJ/Ec<<1
Nakamura…, Nature (1999)
Flux Qubits EJ/Ec>>1
Mooij, Orlando…, Science (1999)
I
pc
| 0 > | 1>
Josephson junction and gauge invariance phase
Makhlin, Schön, Shnirman, RMP (2001)
Vg
CJ EJ
CgCm
charge island
102
1
102
1
Hq Eg zq E J
2 x
q
Hq 4Ec n CgVg
2e
2 EJ cos EcÀ EJ
Ec e2
2C
Decoherence time secs; Rabi Oscillations; Ramsey; two-bit entanglemnet, Nakamura, Devoret, Esteve, Schoekopf,
Superconducting Charge Qubits – Quantum Two Level System
Inserting the Superconducting CavityInserting the Superconducting Cavity
1. To increase the coupling by effectively shorten the distance between the ion and the charge qubit
2. To improve the compatibility by shunting the qubit from the stray photons from the trap
E 1d 0
z,t t n
B cd 0
n z, t
Interaction with Ion, Charge
Cavity
Cavity mode for short distance
Cm: coupling, Cr: Cavity
Hcv 2p cv2
Cr cv
2
2Lr
cv L Rp
2 z
q
Hint 2pcvexCrd i
Cm
Ct
p Qg
Cr
L R
Effective Coupling between Ion and Charge Qubit
Hint e2
Cr
Cm
Ct
xd i
zq
L 100 m
Geometry
Hint 25GHz xd i
zq
R0
d iln d 0
b 0
HdQ Qe|R1 R2 |
4 0R02
Dipole – charge| |
R1
R2
Q
zs z
q
HdQ Qe|R1 R2 |
4 0R0d iEnhanced dipole – charge
| |
R1
R2
QR0
d i
zs z
q
Realization -- with superconducting devices
• Coupling with the motion of trapped ions• Hybrid qubit – superconducting charge qubit, double dot qubit• Quantum trap – EM modes in superconducting cavity
• Exchange information between ion qubit and charge qubit• Decoherence• Scalability
Fast Gate for Exchange Qubit StatesFast Gate for Exchange Qubit States
1. Fast phase gate independent of motional state2. Gate time much shorter than
-1 T~20 nsec with t1,2=5nsec
q1
t1 t2
q2 q1 q2
t 0 t
Pulse sequence
U0t exp i tâx âx
U lzlnl exp izlklnl zs x
n l R s
Uq q exp i q zqx
at
Superconducting Switch for Coupling
Cr/2
Lr
VgCm
CJ EJ
Cg
EJa
ex
Cr/2
ion trap
ex=0/2, no coupling between ion and charge qubitex < 0/2 e.g., nonzero coupling4 cos (ex/0)Ica/0Ca À 0
2 : coupling the same as previous oneRef: Tian,Blatt,Zoller, preprint --
• speed limited by speed of switching flux in the SQUID loop• other switches: SSET, -junction, …• more work needed to better manipulate the coupling
a
Makhlin, Schön, Shnirman, RMP (2001)
Quantum Trap -- Schematic Circuit of Ion Trap, Cavity, Ion Trap
Vi
Vib
Vtrap
Vi
Vib
Vtrap
ion trap ion trapsuperconducting
cavity
Note earlier work -- Heinzen,Wineland, PRA (1990).
Allowing distant ions to communicate …
Hi i Hs1 Hs
2 e2
2Cr 2Cix 1x 2
d i2
Hinti i 25GHz
x 1
x 2
d i2
L 100 m
=L
Effective Coupling between Ions Increased-- electrodes effectively shortens the distance between ions
| | | |R0
Dipole – dipole
Hd d e2dR2
4 0R03
z1s z2
s
| | | |R0
d i d i
=L Hd d e2dR2
4 0R0d i2 z1
s z2s
Enhanced dipole – charge
R0
d i
2ln d 0
b 0
DecoherenceDecoherence
Decoherence of cavity under radiation: • Spin-oscillator-boson bath model• Calderia-Leggett approach: J0 of Rr
induces Jeff on qubit -- Jeff/ Zeff()• With nW scattered photons, radiates for
100 nsec,
• This is not dominate effect
Zeff =Cr Cm /4
Lr Rr
Grabert et al, Phys. Rep. (’88) rq R r
R k
2kBT
Cm
2Ct
2 50m sec2
1. Noise on ion: motional state damping;spontaneous emission…
2. Noise on charge qubit: charge noiseflux noise…
3. Noise on cavity: no dissipation at low temperature well below the gap; how about under laser radiation ?
qubit cavity reservoir
z x j
Jeff
cv
ScalabilityScalability
1. small clusters of ions coupling with two charge qubits • individual addressing to select ions of operation• two bit gate via the charge qubits by selecting two ions
Ref: Tian,Blatt,Zoller, preprint --
switch
couplinglaser addressing
2. small clusters of ions coupling with two charge qubits • electrodynamic coupling of charge qubits in different cluster • gate between ions in different cluster
connecting circuitry
flux flux
ScalabilityScalability
Other aspects of connecting with solid-state systemsOther aspects of connecting with solid-state systems
• manipulating solid-state systems via coupling with ion --- ion coupling with charged Carbon nanotube, 1. quantum state engineering of mechanical motion of the nanotube 2. preparing pure state of nanotube mode by laser cooling 3. entanglement between two nanotubes via laser manipulation of ion: arbitrary states and -- |1,2i +|1,2i
Ref: L. Tian and P. Zoller, quantum-ph/0407020
• manipulating solid-state systems with ideas in quantum optics --- “laser cooling” of nanomechanical resonator 1. Capacitive coupling between charge qubit and resonator 2. Cooling of resonator to ground state via pumping of charge qubit
Other aspects of connecting with solid-state systemsOther aspects of connecting with solid-state systems
beam
Cooper pair box
I. Martin,Shnirman,Tian,Zoller,PRB(04)
r/4
4
r/2
r/4
|, 0
|, 1 |, 0
|, 2 |, 1
|, 3 |, 2
Summary
We studied the interfacing of the ion trap qubit withsolid-state systems:
1. a hybrid qubit can be made of a trapped ion coupling with charge qubit via electrostatic interaction;2. distant ions can couple via the quantum modes of the electrode;3. decoherence and scalability are studied;4. interfacing can provide manipulation of solid-state systems: mechanical modes of nanotubes, resonators
top related