Quantum RatchetsQuantum Ratchets

Quantum Electronics For EngineersQuantum Electronics For Engineers

Instructor: Joel TherrienInstructor: Joel TherrienPresented By Ravi BhatiaPresented By Ravi Bhatia

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What’s a Ratchet?What’s a Ratchet?

• A device which allows motion in one A device which allows motion in one direction.direction.

• Consists of a gear with Asymmetric Consists of a gear with Asymmetric Teeth and a Locking Mechanism that Teeth and a Locking Mechanism that allows the gear to move in one allows the gear to move in one direction only.direction only.

• Everyday Examples: Screwdrivers & Everyday Examples: Screwdrivers & Winches, Bicycle Transmissions.Winches, Bicycle Transmissions.

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Feynman RatchetFeynman Ratchet

• A thought Experiment by Richard Feynman, A thought Experiment by Richard Feynman, ‘Lectures on Physics’, 1963.‘Lectures on Physics’, 1963.

• Can we obtain directed motion from random Can we obtain directed motion from random thermal fluctuation of particles? thermal fluctuation of particles?

• Dream of the Free Energy!Dream of the Free Energy!

• System consists of a microscopic ratchet and System consists of a microscopic ratchet and vane placed in equilibrium, such that it is vane placed in equilibrium, such that it is affected by the random motion of gas affected by the random motion of gas particles hitting the vane. particles hitting the vane.

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Microscopic Ratchet and Vane Microscopic Ratchet and Vane MechanismMechanism

• Asymmetric teeth make the ratchet move in one direction Asymmetric teeth make the ratchet move in one direction under random collisions of gas molecules.under random collisions of gas molecules.

• Direct Violation of the Second Law of Direct Violation of the Second Law of Thermodynamics. Not Possible!Thermodynamics. Not Possible!

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Key Properties of Ratchet Key Properties of Ratchet EffectEffect

• Ratchet Effect: The ability to get directed Ratchet Effect: The ability to get directed motion or transport from random motion or transport from random fluctuations of particles.fluctuations of particles.

• The System must not be in Thermal The System must not be in Thermal Equilibrium -> Obey the Second Law of Equilibrium -> Obey the Second Law of Thermodynamics.Thermodynamics.

• The System must have Asymmetric Spatial The System must have Asymmetric Spatial Symmetry -> Asymmetric Ratchet teeth, Symmetry -> Asymmetric Ratchet teeth, Asymmetric potential.Asymmetric potential.

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Ratchet Effect in ElectronicsRatchet Effect in Electronics

• Using Noise to achieve rectified current.Using Noise to achieve rectified current.• Electrons in an asymmetric but spatially periodic Electrons in an asymmetric but spatially periodic

potential wells.potential wells.• Random Diffusion of electrons is converted into a Random Diffusion of electrons is converted into a

net motion to the left.net motion to the left.• Thermal equilibrium broken by switching ratchet Thermal equilibrium broken by switching ratchet

potential on and off.potential on and off.

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Quantum Tunneling Quantum Tunneling RatchetsRatchets

• Asymmetric Potential implemented Asymmetric Potential implemented using Semiconductor using Semiconductor Heterostructures.Heterostructures.

• MBE growth of Alternating MBE growth of Alternating GaAs/AlGaAs Layers.GaAs/AlGaAs Layers.

• Band bending due to conduction Band bending due to conduction band offset produces a triangular band offset produces a triangular shaped potential well.shaped potential well.

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AlGaAs/GaAs AlGaAs/GaAs HeterostructureHeterostructure

• Fig a) Offset in conduction band causes electrons Fig a) Offset in conduction band causes electrons to flow down to the GaAs layer.to flow down to the GaAs layer.

• Fig b) Only the first Level is populated at Fig b) Only the first Level is populated at cryogenic temperatures forming a 2DEG.cryogenic temperatures forming a 2DEG.

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Behavior of Tunneling Behavior of Tunneling Ratchets Ratchets

• Rectification of a randomly varying Rectification of a randomly varying signal.signal.

• Electron Flow direction is a function Electron Flow direction is a function of Temperature.of Temperature.

• Positive Voltage to the ratchet makes Positive Voltage to the ratchet makes the wells to the right shallower.the wells to the right shallower.

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• High Temperature: Positive voltage causes high energy High Temperature: Positive voltage causes high energy electrons to predominantly move to the rightelectrons to predominantly move to the right

• Low Temperature: Electrons tunnel through the barrier and Low Temperature: Electrons tunnel through the barrier and move to the Leftmove to the Left

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What Have We Achieved using What Have We Achieved using Quantum Tunneling Ratchets?Quantum Tunneling Ratchets?

• Fundamentally Opposite Quantum Fundamentally Opposite Quantum and Classical Behavior.and Classical Behavior.

• Tunneling contributes to the particle Tunneling contributes to the particle flow at low temperatures.flow at low temperatures.

• Rectification of Random Signals or Rectification of Random Signals or Noise at Cryogenic or High Noise at Cryogenic or High Temperatures.Temperatures.

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ReferencesReferences

• ‘‘Mesoscopic Quantum Ratchets and the thermodynamics of Mesoscopic Quantum Ratchets and the thermodynamics of Energy Selective Electron Heat Engines’, Doctoral Thesis, Energy Selective Electron Heat Engines’, Doctoral Thesis, Tammy E. Humphrey,2003, Univ of New South Wales.Tammy E. Humphrey,2003, Univ of New South Wales.

• ‘‘Quantum Clockwork’, New Scientist 2000, Michael Brooks.Quantum Clockwork’, New Scientist 2000, Michael Brooks.• ‘‘Quantum Ratchets’, Doctoral Thesis,2005, Joel Peguiron. Quantum Ratchets’, Doctoral Thesis,2005, Joel Peguiron. • ‘‘Theory of Chaotic Hamiltonian Ratchets’, Doctoral Thesis, Theory of Chaotic Hamiltonian Ratchets’, Doctoral Thesis,

Mathhew R. Sherwood,2004, University of London.Mathhew R. Sherwood,2004, University of London.

• How about free Perpetual Energy? How about free Perpetual Energy? http://home.wanadoo.nl/perpetual/index.htmlhttp://home.wanadoo.nl/perpetual/index.html