Electron interferometry in quantum Hall edge channels Jérôme Rech Centre de Physique Théorique, Marseille in collaboration with C. Wahl, D. Ferraro, T. Jonckheere and T. Martin I out R I out L 1 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Photons ↓ Electrons 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Light beam Photons ↓ ↓ Electrons 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Light beam Photons ↓ ↓ Chiral edge QHE Electrons 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Light beam Beam-splitter Photons ↓ ↓ ↓ Chiral edge QHE Electrons 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Light beam Beam-splitter Photons ↓ ↓ ↓ Chiral edge QHE Electrons Point contact 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Light beam Beam-splitter Coherent light source Photons ↓ ↓ ↓ ↓ Chiral edge QHE Electrons Point contact 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Light beam Beam-splitter Coherent light source Photons ↓ ↓ ↓ ↓ Chiral edge QHE Single electron source Electrons Point contact 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Light beam Beam-splitter Coherent light source Photons ↓ ↓ ↓ ↓ Chiral edge QHE Single electron source Electrons Point contact Mesoscopic capacitor [Fève et al., Science (’07)] Surface acoustic waves [Hermelin et al., Nature (’11)] [McNeil et al., Nature (’11)] Quantum turnstiles [Giblin et al., Nature Comm.(’12)] Lorentzian pulses [Dubois et al., Nature (’13)] 2 / 13
Electronic quantum optics in quantum Hall systems Quantum optics analogs with electrons, i.e. the controlled preparation, manipulation and measurement of single excitations in ballistic conductors INGREDIENT LIST Light beam Beam-splitter Coherent light source Photons ↓ ↓ ↓ ↓ Chiral edge QHE Single electron source Electrons Point contact Mesoscopic capacitor [Fève et al., Science (’07)] Surface acoustic waves [Hermelin et al., Nature (’11)] [McNeil et al., Nature (’11)] Quantum turnstiles [Giblin et al., Nature Comm.(’12)] Lorentzian pulses [Dubois et al., Nature (’13)] ➙ opens the way to all sorts of interference experiments! 2 / 13
Hong-Ou-Mandel interference experiment Two-photon interferences two identical photons sent on a beam-splitter necessarily exit by the same output channel ➙ signature of bosonic statistics 3 / 13
Hong-Ou-Mandel interference experiment Two-photon interferences two identical photons sent on a beam-splitter necessarily exit by the same output channel ➙ signature of bosonic statistics Interference experiment [Hong, Ou and Mandel, PRL 59, 2044 (’87)] counts occurrences of photons present in the two output channels dip is observed when photons arrive at the same time signatures of incoming wave packets 3 / 13
Hong-Ou-Mandel interference experiment Two-photon interferences two identical photons sent on a beam-splitter necessarily exit by the same output channel ➙ signature of bosonic statistics Interference experiment [Hong, Ou and Mandel, PRL 59, 2044 (’87)] counts occurrences of photons present in the two output channels dip is observed when photons arrive at the same time signatures of incoming wave packets Why would it be so different with electrons? they obey fermionic statistics ➙ Fermi sea, hole excitations, ... thermal effects do matter they interact via Coulomb interaction 3 / 13
HOM with electrons: general principle and first results Setup 2 single electron sources I out R counter-propagating channels coupled at QPC I out L measure output currents Single electron source 4 / 13
HOM with electrons: general principle and first results Setup 2 single electron sources I out R counter-propagating channels coupled at QPC I out L measure output currents Single electron source Zero-frequency cross-correlations of output currents � S out dtdt ′ � � I out R ( x , t ) I out L ( x ′ , t ′ ) � − � I out R ( x , t ) �� I out L ( x ′ , t ′ ) � RL = � 4 / 13
HOM with electrons: general principle and first results Setup 2 single electron sources I out R counter-propagating channels coupled at QPC I out L measure output currents Single electron source Zero-frequency cross-correlations of output currents � S out dtdt ′ � � I out R ( x , t ) I out L ( x ′ , t ′ ) � − � I out R ( x , t ) �� I out L ( x ′ , t ′ ) � RL = � Theory at ν = 1 [Jonckheere et al. Phys. Rev. B 86, 125425 (’12)] When electrons arrive independently 1 S RL : sum of the partition noise 0 . 8 S HOM / 2 S HBT flat contrib. ➙ random partitioning 0 . 6 When electrons arrive simultaneously 0 . 4 S RL = 0 ➙ HOM/Pauli dip 0 . 2 D = 0 . 2 D = 0 . 5 D = 0 . 8 0 signatures of injected object (overlap) − 120 − 100 − 80 − 60 − 40 − 20 0 20 40 60 80 100 120 δT 4 / 13
HOM with electrons: experimental results Main experimental results [Bocquillon et al., Science 339, 1054 (’13)] ✬ ✩ � ���� �������������������� � � �� ��� �������� � � �� � � � �� � ����������� �������� � � ��� �� ����������������������� � ���� 5 / 13
HOM with electrons: experimental results Main experimental results [Bocquillon et al., Science 339, 1054 (’13)] � As expected ��� ��� Random ¡par**oning C o r r e l a t i o n s ∆ q ✓ Flat background contribution ��� ��� � � ✓ dip for simultaneous injection � ��� ��� � ��� ��� But... How come it does not reach 0? ��� ��� Pauli ¡dip ➙ decoherence effect ��� ��� ���� ���� � ��� ��� � T i m e d e l a y [ p s ] τ 5 / 13
HOM with electrons: experimental results Main experimental results [Bocquillon et al., Science 339, 1054 (’13)] � As expected ��� ��� Random ¡par**oning C o r r e l a t i o n s ∆ q ✓ Flat background contribution ��� ��� � � ✓ dip for simultaneous injection � ��� ��� � ��� ��� But... How come it does not reach 0? ��� ��� Pauli ¡dip ➙ decoherence effect ��� ��� ���� ���� � ��� ��� � T i m e d e l a y [ p s ] τ Something special happens beyond the simple ν = 1 picture 5 / 13
HOM with electrons: experimental results Main experimental results [Bocquillon et al., Science 339, 1054 (’13)] � As expected ��� ��� Random ¡par**oning C o r r e l a t i o n s ∆ q ✓ Flat background contribution ��� ��� � � ✓ dip for simultaneous injection � ��� ��� � ��� ��� But... How come it does not reach 0? ��� ��� Pauli ¡dip ➙ decoherence effect ��� ��� ���� ���� � ��� ��� � T i m e d e l a y [ p s ] τ Something special happens beyond the simple ν = 1 picture Interactions as a source of decoherence ν = 1 5 / 13
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