QUANTUM ELECTRONIC ON THE TRAY* *ur le plateau (de aclay)
Goal: Reveal the quantum behavior of electrons
everal ways of revealing the quantum behavior of electrons 1 Interference experiments of coherent electron waves B 2 Particle-in-a box quantum energy levels of artificial atoms 3 Interaction via exchange of light quanta with environment?
Interference of electrons in vacuum Change phase with Aharonov Bohm flux In an electron microscope http://www.hqrd.hitachi.co.jp/em/doubleslit.cfm Detector Interference pattern builds up on detector. What about in solids? 4
Electron interference in solids? Does disorder destroy interference? Defects What modulates electron interference? Aharonov Bohm flux modulates the phase: j =-2p F/F 0 F=B creen? creen=resistance Constructive or desctructive interference determine electric 5 transmission
R ( ) Electron interference in micron-size rings F=B Magnetic flux modulates transmission Ring in a two dimensional electron «gas» (D. Mailly, LPN Marcoussis) 7200 7000 6800 6600 1 micron 6200-400 -300-200 -100 0 100 200 300 400 A (small) fraction of resistance is modulated by a magnetic field! 6400 T=0.05 Kelvin champ magnétique B (Gauss) 6
Much more than resistance: all quantum properties are modulated by magnetic flux F ext E j =-2p F ext /F 0 0 p 2 2p j Phase dependent electron spectrum Consequence= persistent current in ring (non superconducting), I persistent =-de/df Contactless detection of these currents: Mesoscopic Physics Group, LP Orsay (H. Bouchiat)
Interference between 1D Quantum Hall edge states Disordered 2D conductor in zero magnetic field Many diffusive trajectories Disordered 2D conductor in high magnetic field B Quantum Hall edge states Propagate ballistically, as if no disorder uantum Hall edge states perfect for interference experiments
Interference between 1D Quantum Hall edge states Mach Zender interferometer in a 2D «electron gas» B Ballistic Quantum Hall edge states Quantum interference over several tens of micrometers. Can change length of path with V G NanoElectronics group, PEC, CEA aclay Quantum Transport group, LPN Marcoussis What limits interference: interaction between edge states (many body, not independent)?
Density of states x occupation Another way to control phase: use superconductors uperconductors have a fixed phase Macroscopic wavefunction y BC =De ij Cooper pairs +k, -k, A gap D in the spectrum, and R=0 Energy Empty quasiparticle states D 0 -D No single particle states at low energy: only paired electrons Occupied quasiparticle states
Two superconductors impose interesting boundary conditions: a gap and a phase difference,j 1 Disordered non wire,j 2 Phase difference controls all properties of junction
uperconductors impose phase difference and induce entanglement between pairs of electrons,j 1 Disordered non wire,j 2 A phase dependent gap appears due to quantum interference gap No gap gap + + 0 p 2p j 0 p 2p j Phase dependent spectrum with gap due to entanglement of pairs of electrons: upercurrent
Pair correlations induced in all sorts of conductors metals Ferromagnets Meso group LP Orsay;,D,De ij 1 DNA Au, Cu, Ag graphene,d Molecules with spins,j 1,j 2 carbon nanotube A single atom! N2 group LP Orsay; Quantronics group CEA aclay; Theory group LP Orsay; Theory group Polythechnique
Guessing game What s what? Physique mésoscopique LP Orsay Physique mésoscopique LP Orsay 300 nm Quantronique CEA aclay 1 mm
2 Particle-in-a box quantum energy levels of artificial atoms Carbon nanotubes: 2 levels! Meso group LP Orsay Transport via orbitals of real atoms Quantronics group CEA aclay Discrete levels in electron box Quantum dots: a small electron box Quantum Transport, LPN Marcoussis Questions: Probe quantum states of these systems. Magnetism, superconductivity, correlations via such a small number of channels?
2 Particle-in-a box quantum energy levels of artificial atoms Classical Just two levels: Form a quantum bit In practice, quantum bits = artificial atoms made of superconductors Quantronics group CEA aclay
Example of processor with two qbits Qubit= Jonction Josephson + Capacitor Quantronics group, aclay
3 Interaction via electromagnetic (light) quanta with environment? Current fluctuations in conductor : NOIE Intrinsic noise reveals transport properties of conductor : Low frequency: can reveal discreteness of electron charge and statistics High frequency (>1 GHz: hw>>k B T), realm of quantum optics: Electronic fluctuations within conductor can be seen as photons. Photon frequency= knob to probe dynamics and energy of conductor. Entanglement of emitted photons? Difference between emission and absorption? Reveal dynamics of systems and energy spectrum Can outer circuit modify (via photon exchange) electronic fluctuations?
Interaction via electromagnetic (light) quanta with environment? Emission w<0 Mesoscopic system Absorption w>0 insulator On-chip quantum detector (counts photons, up to 100 GHz) Meso group LP Orsay Theory group LP Orsay Detect very high frequency noise of quantum system. ensitive to difference between emission and absorption (hw>>kt ) Reveal dynamics of systems and energy spectrum
Interaction via electromagnetic (light) quanta with environment? electrons photons Mesoscopic system Quantum transport, LPN Marcoussis Quantronics, CEA aclay NanoElectronics, CEA aclay Impedance Z(w) Circuit in which system is embedded can change (via photon exchange) resistance of mesoscopic system!
Interaction via electromagnetic (light) quanta with environment? Current fluctuations generate photons: Detection via rf circuit or optical detection NanoElectronics, CEA aclay N2, LP Orsay Measure both electron transport and photon emission from quantum circuit (correlation)
Theory group (LP Orsay) G. Montambaux I. afi P. imon C. Bena J.N. Fuchs M. Gabay Quantum Transport (LPN Marcoussis) F. Pierre A. Anthore D. Mailly Meso group (LP Orsay) H. Bouchiat R. Deblock M. Ferrier. Guéron A. Kasumov N2 (LP Orsay) J. Gabelli M. Aprili C. Quay Theory (X) A. Georges K. LeHur Quantronics (CEA aclay) D. Estève H. Pothier C. Urbina P. Berthet D. Vion P. Joyez NanoElectronic (CEA aclay) P. Roche C. Glattli F. Portier