How to Operate Circuits Quantum Mechanically? · Cooper Pair Box Qubit 5 m [Bouchiat, Vion, Joyez,...
Transcript of How to Operate Circuits Quantum Mechanically? · Cooper Pair Box Qubit 5 m [Bouchiat, Vion, Joyez,...
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How to Operate Circuits Quantum Mechanically?
Review: M. H. Devoret, A. Wallraff and J. M. Martinis, condmat/0411172 (2004)
recipe:
• avoid dissipation
• work at low temperatures
• isolate quantum circuit from environment
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Quantum Harmonic Oscillator at Finite Temperature
10 GHz ~ 500 mK
low temperature required:
E
20 mK
thermal occupation:
|0
|1|2
|n
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Internal and External Dissipation in an LC Oscillator
impedance
quality factor
internal losses:conductor, dielectric
external losses:radiation, coupling
total losses
excited state decay rate
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Resonator Quality Factor and Photon Lifetime
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Controlling Coupling to the E.M. Environment
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How to Make Use of the Josephson Junction in Qubits?
current bias flux biascharge bias
different bias (control) circuits:
phase qubit flux qubitcharge qubitR
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The Cooper Pair Box …… a charge qubit.
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Cooper Pair Box Qubit
5 m
[Bouchiat, Vion, Joyez, Esteve, Devoret, Physica Scripta T76, 165 (1998).]
bulk
island
v
superconducting island connected via Josephson junctions to grounded reservoir (bulk)
Cooper pairs can tunnel onto island relevant degree of freedom: number of Cooper pairs on island (N) polarization charge adjustable via voltage bias energy scales: charging energy EC (energy to add another Cooper pair)
Josephson energy EJ (coupling energy)
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Josephson energy:
Charging energy:
Gate charge:
A Charge Qubit: The Cooper Pair Box
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Questions:
How does the charge configuration (charge on island) of the system change, when the bias voltage is tuned slowly from V(0)=0 to V(t) = Vf? In particular, what happens at ng=0.5?
What’s the relevant timescale for ‘slow’? And what happens, if the voltage is tuned faster?
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Two State Approximation
Shnirman et al., Phys. Rev. Lett. 79, 2371 (1997)
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Tuning the Josephson Energysplit Cooper pair box in perpendicular field
SQUID modulation of Josephson energy
[J. Clarke, Proc. IEEE 77, 1208 (1989)]
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Transmon qubit – a charge noise resilient qubit
• shunting capacitor reduces Ec
• Increased EJ/ Ec ratio flattens energy bands
• Less sensitivity to charge noise
[Koch et al. PRA 76, 042319 (2007); Schreier et al. PRB (2008)]
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Transmon qubit – tuning of transition frequency
transition frequency can be adjusted by external flux bias
[Koch et al. PRA 76, 042319 (2007); Schreier et al. PRB (2008)]
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Cavity QED with Electronic Circuits
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Free Atom
[D. Walls, G. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994)]
weak interaction with single photons:
• dipole moment d (usually small in atoms ~ ea0)
• single photon fields E0 (small in 3D)
• photon/atom interaction (usually small)
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Cavity Quantum Electrodynamics
[D. Walls, G. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994)]
interaction of atom and photon in a cavity
Jaynes-Cummings Hamiltonian
strong coupling limit:
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Dressed States Energy Level Diagram
Atomic cavity quantum electrodynamics reviews:J. Ye., H. J. Kimble, H. Katori, Science 320, 1734 (2008)
S. Haroche & J. Raimond, Exploring the Quantum, OUP Oxford (2006)