josephson junction qubits
DESCRIPTION
Josephson Junction Qubits. Alex Hegyi Justin Ellin Andrew Chan. Classical Resistance (Review). Metals In a metal, the electrons are shared by atoms in a lattice. This sea of electrons is free to travel along the entire lattice. Dissipation - PowerPoint PPT PresentationTRANSCRIPT
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Josephson Junction Qubits
Alex HegyiJustin Ellin
Andrew Chan
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Classical Resistance (Review)
Metals In a metal, the electrons are shared by atoms in a lattice. This sea of electrons is free to travel along the entire lattice.
Dissipation Caused by inter-electron/ion interactions or other atoms, resulting
in heat (dV) = (dI)R, R = pL/A (p resistivity, length, cross-sectional area) P = IV Prevents indefinite propagation of currents, analogous to friction
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Superconductors
Superconductor Properties State characterized by zero (exactly) electrical resistance Meissner Effect – weak external fields only penetrate small
distances (London skin Depth) Type I – Superconductivity destroyed abruptly when field
reaches critical value Type II – additional critical temperature which permits
magnetic flux but still no electrical resistivity Generation of a current to cancel external field
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BSC Theory Fermi Energy
The lowest energy of the highest occupied quantum state at absolute zero was considered to be the Fermi Energy
Where N/V is the density of fermionsThis can be derived by considering a 3-dimensional square box.
BSC- Bardeen, Cooper, and Schrieffer 1957 The theory essentially accounts for an energy level even
below this threshold. The gap between this energy level and the fermi energy
accounts for many of the properties of superconductors Whereas before the electron could be excited in a continuous
spectrum of possible energy interactions (and interchange/lose energy with lattice and other electrons), there is now a discrete energy gap.
The excitations become forbidden and the electron sees no “obstacles” or no resistance! But what accounts for this gap?
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Cooper Pairs The atoms in a lattice are not fixed Free electrons are repulsed from other electrons but are able to
attract and distort the positively charged nucleus. This distortion in turn attracts other electrons.
Coupling (on the order of fractions of an eV) usually broken by thermal energy or coulomb interaction.
When the thermal energy is low, T ~ 5K, this dominates effectively linking electrons in pairs to each other even over “large” distances .
The electrons pair up with those of opposite spin. Exclusion principle no longer applies. All electron pairs condense into
this bound state energy.
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Two Notes on Modern Superconductors
Current Lifetime – occasionally interactions may result that do go across the gap.
Experimentally, currents on superconductors can perpetuate for upwards of tens of thousands of years.
Theoretically, could last longer than the known age of the universe.
High Temperature Superconductors –superconductors that can’t be explained by BCS because state achieved well above fermi levels
(Sn5In)Ba4Ca2Cu10Oy: superconducting at ~200K (Dry ice is about this range)
How do they work?
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Josephson Junction Brian David Josephson proposed (1964) sandwiching an insulator
between two superconductors. Provided separation is small, current will tunnel through the
barrier However when the current reaches a certain critical value then a
voltage will develop across the junction which will in turn increase the voltage further.
The frequency of this oscillation is ~ 100 GHz Below this critical current, no voltage. Above, oscillating voltage.
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Some Uses of Junctions
SQUIDs (superconducting quantum interference devices)
Precise Measurements
Voltage to Frequency Converter
Single-Electron Transistors
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Flux Qubit
Quantum state is stored in the direction of the current |0> is counter-clockwise |1> is clockwise
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Manipulate State
Requires a constant external magnetic flux Flux determines the energy difference
between the two states Apply a microwave pulse
Causes the flux qubit to oscillate between ground state (|0>) and excited state (|1>)
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SQUID
Superconducting Quantum Interference Device
Critical Current
Below:
Current flows without voltage
Above:
Oscillating current develops
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Measurement
Apply a current pulse to SQUID Collapses state
Magnetic flux through flux qubit determines critical current of SQUID
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Qubit Interaction
Entanglement between two qubits is achieved by coupling their fluxes
Superconducting bus Transfers a quantum state from one
qubit to another by sending a single photon along a superconducting wire
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“Additional” DiVincenzo Criteria
Conversion of stationary, flying qubits Optical Microcavities, Cavity QED
Transmission of flying qubits Fiber Optics
Microwave transmission lines (Circuit QED)—way to accomplish the above in case of superconducting qubits*
*Wallraff et al., Nature, 431, 9 Sept. 2004
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Strong Coupling/Cavity QED
Two-level quantum system coupled to electromagnetic cavity
“Strong Coupling” characterized as coherent exchange of excitation between cavity, quantum system i.e., coherent conversion between
stationary, flying qubit Model—Two SHOs connected by
weak spring
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Microwave Resonator/Qubit System
*Schoelkopf and Girvin, Nature, 451, 7 Feb. 2008
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Quantum Communication
If energy difference between |0> and |1> resonant with cavity, energy exchanged (Rabi rotation)
If off-resonant (dispersive) energy not exchanged
Align qubits along transmission line, tune energy difference (using gate bias, flux bias) to control interaction with line
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Microwave Resonator/Qubit System
*Wallraff et al., Nature, 431, 9 Sept. 2004