Interfacing quantum optical and solid state qubits Cambridge, Sept 2004 Lin Tian

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

Hybrid Qubit -- Schematic Circuit of Ion, Cavity,Charge Qubit

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

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

Interfacing quantum optical and solid state qubits Cambridge, Sept 2004 Lin Tian

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