Microwaves for quantum simulation in superconducting circuits and semiconductor quantum dots

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1 Microwaves for quantum simulation in superconducting circuits and semiconductor quantum dots Christopher Eichler ScaleQIT Conference, Delft In collaboration with: C. Lang, J. Mlynek, Y. Salathe, S. Schmidt, J. Butscher, P. Kurpiers, A. Wallraff (ETH Zurich) K. Hammerer, T. Osborne (Universität Hannover) Y. Liu, J. Stehlik, J. Petta (Princeton University) Princeton University

2 Solid State Systems for Quantum Control Defects & Donors in solids (e.g. NV centers) Jelezko et al., PRL (2004) Opto- and electromechanics Aspelmayer et al., RMP (2014) Gate-defined/Self-assembled Quantum Dots (2DEG, nanowire, CNT, SiGe) Superconducting circuits A. Wallraff et al., Nature (London) 431, 162 (2004) R. J. Schoelkopf, S. M. Girvin, Nature (London) 451, 664 (2008) Wiel et al., RMP ( 2003) Hanson et al., RMP (2007) and many more.

3 EM Radiation for Quantum Control and Measurement Control with EM radiation (Optical, Microwave, RF, ) Quantum System Readout & probe system Exhibit Quantum correlations! Use radiation fields as a quantum register for QIP Here: Simulate GS of interacting bose gas in 1D

4 Quantum Simulation describes physical system of interest (physics, chemistry, biology, ) encodes hard classical problem interesting toy model use universal quantum computer still to be realized! simulating a quantum system OR difficult on classical computer! map! quantum simulator sufficient controllability, flexibility! Feynman, Int. Journal of Th. Phys. 21, 467 (1982) Llloyd, Science 273, 5278 (1996)

5 Systems for Quantum Simulation Ultracold gases Trapped ions more established Optical photons Bloch et al., Nat. Phys. 8, 267 (2012) Nuclear magnetic resonance Microcavity Polaritons Deng et al., RMP 82, 1489 (2010) Kasprzak, Nature (2006) Blatt & Roos, Nat. Phys. 8, 277 (2012) under development Solid state quantum devices Aspuru-Guzik & Walther, Nat. Phys. 8, 258 (2012) Vandersypen & Chuang, RMP 76, 1037 (2004) Georgescu et al., RMP 86, 153 (2014)

6 Find Ground State of Hamiltonian Typically: Quantum system Cooling or Annealing Ground state How about flexibility?

7 New Paradigm for Quantum Simulation Alternative: Ground state well described by Specific class of states: - Matrix product states (MPS) - Projected entangled pair states Verstraete, Murg & Cirac Advances in Physics (2008) Not necessarily identical! Use to create Controllable quantum system

8 Variational Quantum Simulation using Cavity QED 1) Generate radiation emulating MPS state 2) Program simulated Hamiltonian into measurement apparatus. Measure 3) Vary state using external control Proposal: Barrett et al., PRL 110, (2013)

9 What we Simulate Here: Gas of interacting bosons in 1D Described by the Lieb-Liniger model kinetic energy repulsive interaction chemical potential only one parameter in the model! Lieb & Liniger Phys. Rev. 130, 1605 (1963) Paredes et al., Nature 429, 277 (2004)

10 What is needed? 1) Tunable open quantum system: SC circuit realization 2) Efficient & programmable measurement apparatus 3) Simulation of the Lieb-Liniger model

11 Cavity QED with Superconducting Circuits cavity Cavity transmission line resonator Atom Josephson junction atom small mode volume (1D) large dipole moments strong coupling A. Blais, et al., PRA 69, (2004) A. Wallraff et al., Nature (London) 431, 162 (2004) R. J. Schoelkopf, S. M. Girvin, Nature (London) 451, 664 (2008)

12 Circuit QED Device with Tunable Coupling Transmon Out In asymmetric resonator coupling control using global field + local flux line tunable frequency and tunable coupling Local flux line Srinivasan et al., PRL 106, , (2011)

13 Spectroscopic Cavity Measurements measure transmission tunable & stable cavity QED system individual control of coupling & frequency Tune at Tune at

14 Measurement Apparatus At GHz frequencies? Lieb-Liniger Hamiltonian Field operator Radiation field Cavity output field Measure photon correlation functions!

15 Microwave Photon Field Detection in the visible x x No photon counters yet for microwaves! much smaller photon energy: instead: linear amplifiers/adc signal processing

16 Experiments with Propagating Quantum Microwaves Time-correlations functions for continuous single photon source Lang et al., PRL 107, (2011) Bozyigit et al., Nat. Phys 7, 154 (2011) Eichler et al., PRL 106, (2011) since then experiments on: Squeezing Wigner Tomography Qubit-Photon-Entanglement Hong-Ou-Mandel interference Photon shaping Superradiance Quantum Dot Lasing See ETH Qudev & Princeton Petta lab publications improved detection efficiency with quantum limited amplifiers linear amplifier adds vacuum/thermal noise Quantum limited amplifiers: (Special requirements in terms of dynamic range, bandwidth, phase-insensitivity) Eichler et al., PRL (2014) c.f.: Castellanos-Beltran et al., Nat. Phys. 4, 929 (2008) Bergeal et al., Nature 465, 64 (2010) Macklin et al., Science (2015) reduce g (2) measurement time by ~10000

17 Simulate Lieb-Liniger Hamiltonian How to measure? Barrett et al., PRL 110, (2013)

18 Time-resolved Correlation Measurements Drive nonlinear cavity mode vs. two variational parameters: Drive rate Effective anharmonicity: Energy in variational space

19 Measured Energy Landscape Energy landscape vs. variational parameters: Local minimum in variational space Ground state depends on interaction strength v variational ground state Parametric Amplifier reduces measurement time by ~10000

20 Properties of the Simulated Ground State Ground state energy vs. interaction strength Experimentally obtained Tonks-Giradeau limit Exact numerical result We can do more than that: We can probe any quantity of interest! at particle density Eichler et al., PRX 5, (2015)

21 Properties of the Simulated Ground State Experimentally obtained first order correlation function: Conversion of temporal into spatial coordinates Decrease of correlation length with increasing interaction strength Numerical result with small D similar to experimental data Eichler et al., PRX 5, (2015)

22 Properties of the Simulated Ground State Experimentally obtained particle-particle correlations: crossover from weakly interacting Bose gas to Tonks-Giradeau gas anti-bunching reveals fermionization qualitative agreement already for a simulation with two variational parameters! Eichler et al., PRX 5, (2015)

23 What tools are behind it? G Photon Quantum limited amplifiers statistics

24 Maser emission from double quantum dot device 1 mm S D 500 nm Photon D S S D Quantum Dot Gain Medium Y. Liu, J. Stehlik, CE, et al., Science 347, 285 (2015) M. Delbecq et al., PRL 107, (2011) T. Frey et al., PRL 108, (2012) MASER? statistics C. Eichler, et al., PRL 106, (2011) C. Eichler et al., PRA 86, (2012)

25 Photon Statistics below and above threshold Counts Off/On 10 Data Poisson Thermal Q 0 p n (%) Counts 0 On/On I n Data Gaussian Q 0 p n (%) I Liu, Stehlik, CE, et al., Science 347, 285 (2015) n C. Eichler, et al., PRL 106, (2011)

26 Interdisciplinary connections revealed Highly flexible platform Desirable scalability features High level of control/tunability: Many-body physics Biophysics Quantum information theory Extension to higher dimensions Efficient correlation measurement Quantum field theories Discrete Lattice models Vector fields Fermionic systems