Interfacing quantum optical and solid state qubits

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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)

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• Ion Trap -- charged particles in electromagnetic
  potential
• Harmonic confinement, laser manipulation

Motional degree Internal degree

• 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)

red side band -- blue side band d0
detuning h kD x 0.1, W lt wn
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Ion Trap Quantum Computing

• Internal state of trapped ion as qubits
• Center of mass motion as media
• Swap states of spin and motion

Cirac and Zoller (95).
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
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Scalable Ion Trap Schemes by Moving Ions
Segmented trap
Moving head
-- Cirac, Zoller (00)
-- Kielpinski, Monroe, Wineland (02)
Scalable ion trap quantum computing without
moving ions over long distance?
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• Progress and problems of quantum optical system
  in quantum
• information 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?

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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

• quantum trap approach
• coupling between ion and trap mode
• trap mode is quantum
• effective interaction between ions

• Technical Difficulties ion trap vs charge qubit
• laser of trap affects with charge qubits
• ion trap at low temperature,

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• 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

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Spin-dependent interaction induced by laser
pulses -- mechanism
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Hybrid Qubit -- Schematic Circuit of Ion,
Cavity,Charge Qubit
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Superconducting Qubits
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Superconducting Charge Qubits Quantum Two Level
System
EcÀ EJ
Makhlin, Schön, Shnirman, RMP (2001)
Decoherence time msecs Rabi Oscillations
Ramsey two-bit entanglemnet, Nakamura, Devoret,
Esteve, Schoekopf, L
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Inserting the Superconducting Cavity

• To increase the coupling by effectively shorten
  the distance
• between the ion and the charge qubit
• To improve the compatibility by shunting the
  qubit from
• the stray photons from the trap

Cavity
Interaction with Ion, Charge
Cavity mode for short distance
Cm coupling, Cr Cavity
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Effective Coupling between Ion and Charge Qubit
Geometry
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• 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

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Fast Gate for Exchange Qubit States
1. Fast phase gate independent of motional
state 2. Gate time much shorter than wn-1
T20 nsec with t1,25nsec
Pulse sequence
at
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Superconducting Switch for Coupling

• FexF0/2, no coupling between ion and charge
  qubit
• Fex lt F0/2 e.g., nonzero coupling
• 4p cos (pFex/F0)Ica/F0Ca À w02 coupling the
  same as previous one
• Ref Tian,Blatt,Zoller, preprint --
• speed limited by speed of switching flux in the
  SQUID loop
• other switches SSET, p-junction,
• more work needed to better manipulate the
  coupling

Makhlin, Schön, Shnirman, RMP (2001)
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Quantum Trap -- Schematic Circuit of Ion Trap,
Cavity, Ion Trap
Allowing distant ions to communicate
ion trap
ion trap
superconducting cavity
Note earlier work -- Heinzen,Wineland, PRA (1990).
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Effective Coupling between Ions Increased --
electrodes effectively shortens the distance
between ions
L
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Decoherence

• Noise on ion motional state damping
• spontaneous emission
• Noise on charge qubit charge noise
• flux noise
• Noise on cavity
• no dissipation at low temperature well
• below the gap how about under laser
• radiation ?

• Decoherence of cavity under radiation
• Spin-oscillator-boson bath model
• Calderia-Leggett approach J0 of Rr
• induces Jeff on qubit -- Jeff/ w Zeff(w)
• With nW scattered photons, radiates for
• 100 nsec,
• This is not dominate effect

Grabert et al, Phys. Rep. (88)
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Scalability

• 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 --
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Scalability

• 2. small clusters of ions coupling with two
  charge qubits
• electrodynamic coupling of charge qubits in
  different cluster
• gate between ions in different cluster

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Other 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 y and c -- y1,c2i
  c1,y2i

Ref L. Tian and P. Zoller, quantum-ph/0407020
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Other aspects of connecting with solid-state
systems

• 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

I. Martin,Shnirman,Tian,Zoller,PRB(04)
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Summary
We studied the interfacing of the ion trap qubit
with solid-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
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