Amplification, entanglement and storage of microwave radiation using superconducting circuits Jean-Damien Pillet Philip Kim s group at Columbia University, New York, USA Work done in Quantum Electronics group, LPA Ecole Normale Supérieure de Paris, France University of Virginia - April 24th 2014 1
Microwave: powerful and versatile platform Standard commercial apparatuses due to decades of use in telecommunica>on Vector Network Analyzer Cable Direc5onal coupler Amplifier Microwave generator Circulator Phase shi@er 2
Processing at single photon level LC circuit Harmonic oscillator 3
A unique component: the Josephson junction Dimensions ~ 100 nm < wavelength ~ 1 cm => metamaterials 4
Josephson circuits Strongly anharmonic oscillator Weakly anharmonic oscillator L J C L 5
State preparation in microwave quantum optics Strongly anharmonic oscillator P. Campagne-Ibarcq et al., PRX 2013 Two-level system M. Devoret et al., Science 2013 6
State preparation in microwave quantum optics Strongly anharmonic oscillator Two-level system Weakly anharmonic oscillator Harmonic oscillator continuous variable 7
State preparation in microwave quantum optics Vacuum state Weakly anharmonic oscillator Coherent state Harmonic oscillator continuous variable 8
State preparation in microwave quantum optics Fock states and superpositions Cavity QED (Haroche, Paris) M. Hofheinz et al., Nature 2010 Schrödinger cats Squeezed vacuum state G. Kirchmair et al., Nature 2013 1-mode F. Mallet et al., PRL 2011 2-mode C. Eichler et al., PRL 2011 9
State preparation in microwave quantum optics Fock states and superpositions Cavity QED (Haroche, Paris) G. Kirchmair et al., Nature 2013 M. Hofheinz et al., Nature 2010 Schrödinger cats High fidelity measurement phase-preserving amplifier Storage of microwave quantum state quantum memory Generation of entanglement over 2 spatially separated modes 1-mode Squeezed vacuum state F. Mallet et al., PRL 2011 2-mode C. Eichler et al., PRL 2011 10
Microwave phase preserving amplifiers best commercial amplifiers (4K) 4K at 2.5 GHz = 40 photons of noise 11
Microwave phase preserving amplifiers best commercial amplifiers (4K) 4K at 2.5 GHz = 40 photons of noise 12
Microwave phase preserving amplifiers best commercial amplifiers (4K) 4K at 2.5 GHz = 40 photons of noise Quantum limited amplifier ½ quantum of noise (Caves, PRD 1982) 13
Three wave mixing at microwave frequencies Lithium Triborate LBO Crystals 14
Three wave mixing at microwave frequencies Classical diode : non- linear and dissipa>ve 15
Three wave mixing at microwave frequencies Jospehson junc>on : non- linear and non- dissipa>ve 16
Josephson mixer 17
Amplification or Conversion Quantum limited amplifier Entanglement source Noiseless frequency converter Tunable coupler 2-mode squeezing operator 18
Amplification or Conversion Basis of quantum limited amplification: Stimulated emission Quantum limited amplifier Entanglement source 2-mode squeezing operator 19
Amplification or Conversion Commercial Basis of quantum limited amplification: Stimulated emission Quantum limited Phase-preserving quantum limited amplifier ½ quantum of noise (Caves, PRD 1982) 2-mode squeezing operator 20
Distributed or lumped resonators λ/2 resonators High Q Bergeal et al., Nature 2010 N. Roch et al., PRL 2012 Lumped elements Low Q Optimal design for amplifier 21
Why lumped is the optimum amplifier? 22
Why lumped is the optimum amplifier? Amplification is a trade off small => non-linearity too weak large => junctions can t sustain few photons 23
Why lumped is the optimum amplifier? 24
Why lumped is the optimum amplifier? 25
Why lumped is the optimum amplifier? High Q => slower, smaller bandwidth Larger bandwidth for similar performance 26
Realization 10 um T=40 mk 27
Setup 28
Characterization of the resonators Measurement of the resonant frequency Pump OFF, G=1 29
Characterization of the resonators Measurement of the resonant frequency C = 3pF L = 360 ph p = 25% Pump OFF, G=1 30
Characterization of the resonators Measurement of the resonant frequency C = 3pF L = 360 ph p = 25% C = 6pF L = 260 ph p = 35% Pump OFF, G=1 C = 3-6pF L = 260-360 ph p = 25-35% Very Large tunability (thanks to large p) 31
Amplification Fixed flux Pump ON - More than 50 MHz at 20dB - One order of magnitude higher than Josephson amplifier with distributed resonator 32
Amplification Pump ON Fixed flux Large bandwith => multiplexing of qubits Low Q => fast enough for Quantum feedback 33
Quantum limited 50 Ohm noise source (controllable temperature) Black body radiation 34
Quantum limited Josephson amplifier Black body radiation 35
Quantum limited Commercial amplifier Black body radiation 36
Quantum limited Commercial amplifier Black body radiation 37
Quantum limited Commercial amplifier Black body radiation 38
Quantum limited T = 50 mk Black body radiation Amplified noise source radiation Less than 0.2 photons of noise Quantum limited amplifier ½ quantum of noise (Caves, PRD 1982) Half photon 0.6 photon => Near quantum limit Minimum Quantum noise Amplifier extra noise 39
Dynamical range Amplifier suitable for few photons measurements 40
Low Q versus high Q Low Q Higher bandwidth Faster Optimal amplifier High Q Longer lifetime resonator Quantum memory 41
Quantum memory for microwave Mechanical resonator High Q 2D cavity Palomaki et al., Nature 2013 Spin ensembles Yin et al., PRL 2013 Zhu et al., Nature 2011 Kubo et al., PRL 2011 42
3D cavity for storage High-Q superconducting cavities G. Kirchmair et al., Nature 2013 Q up to 1 million 43
Quantum memory for microwaves Transmission line (50Ω) Buffer Tunable coupling Memory resonator 44
Quantum memory for microwaves Transmission line (50Ω) Dynamically tunable mirror 45
Quantum memory for microwaves memory cavity 3D superconducting cavity for enhanced storage time 46
Quantum memory for microwaves JJ Fast tunable coupling Josephson Ring 47
Quantum memory for microwaves buffer cavity bandwidth vs efficiency 48
Quantum memory for microwaves down to 40 mk 49
Pulsed experiment? Control field Control field What waveform can the memory capture optimally? waveform released by the memory Control field Control field waveform optimally capture time reverse 50
Quantum memory for microwaves Write the memory Pompe ON => Coupling ON 51
Quantum memory for microwaves Write the memory Pompe OFF ON => Coupling ON OFF 52
Quantum memory for microwaves Read the memory Pompe ON => Coupling ON 53
Coupling OFF Pump OFF time 54
Coupling OFF Pump OFF time 55
Optimal capture ON Pump OFF 56
Optimal capture ON Pump OFF ON 57
Optimal capture and delayed retrieval writing/reading time 58
Quantum memory performance writing/reading time storage time time bandwidth product efficiency 59
Entanglement generation buffer cavity memory cavity transmission line Entanglement generation Generating Entangled Microwave Radiation Over Two Transmission Lines, E. Flurin et al., PRL 2012 60
Entanglement generation Hamiltonian evolution 2-mode squeezing operator Quantum limited amplifier Entanglement source 61
Entanglement generation 62
Retrieval 63
Squeezed cross-correlation 64
Squeezed cross-correlation Eichler et al., PRL 2011 Menzel et al. PRL 2012 points measurement time 65
Experimental results Control field ON 66
Amplification chain noise Uncorrelated noise from the amplifiers 67
Experimental results Control field OFF 68
Experimental results Subtracted ON-OFF histograms 69
Measured covariance matrix 70
Covariance matrix and entanglement witness Logarithmic negativity Purity Entanglement threshold 71
Conclusions Optimal phase preserving amplifier Quantum memory Generation of entanglement on demand Pillet et al., in preparation Flurin, Roch, Pillet et al., arxiv:1401.5622 72
Thanks Vladimir MANUCHARYAN Landry BRETHEAU Michel DEVORET Emmanuel FLURIN Nicolas ROCH Benjamin HUARD François MALLET Philippe CAMPAGNE-IBARCQ 73
Perspectives Pas de pause Pas de repit Marquer le temps entre slides de transi>on 74
Perspectives Teleportation of a quantum state from one memory to another Teleporation 75
Perspectives Teleportation of a quantum state from one memory to another Teleporation 76
Trash 77
Microwave: powerful and versa6le pla7orm rocessed at the single photon level with non- dissipa>ve superconduc>ng In dilu>on fridge T=30mK dd superconduc>ng qubit Transmission line Direc5onal coupler Quantum ampli Circulator Ku et al., Applied Superconduc;vity (2011) Quantum Memory Kamal et al., Nat. Phys. 2011 Sev Palo arxi 78