Non-equilibrium spin systems - from quantum soft-matter to nuclear magnetic resonance

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1 Non-equilibrium spin systems - from quantum soft-matter to nuclear magnetic resonance Igor Lesanovsky Daejeon 24/10/2017

2 Postdocs Federico Carollo Carlos Espigares Perez Ricardo Gutierrez Alexander Karabanov Matteo Marcuzzi Katarzyna Macieszcziak Jiri Minar Pietro Rotondo PhD-students Andreas Kouzelis Eliana Fiorelli Maike Ostmann Federica Raimondi Dominic Rose Local collaborators B. Olmos J. P. Garrahan M. Guta A. Armour W. Li W. Köckenberger Open Experimental Position Assistant/Associate/Professor of Experimental Quantum Physics/Technology Closing date: 31/10/17 Open Theory Position Postdoc in many-body physics Closing date: 26/10/17 External collaborators O. Morsch group (Pisa) S. Diehl group (Cologne)

3 Outline 1),Soft-matter physics with cold atoms - dynamics is more than statics - kinetic constraints - Rydberg atoms - experiments 2) Non-equilibrium phase transition - contact process or game of life - experimental results - competing classical an quantum effects - quantum epidemics 3) Non-equilibrium magnetic resonance - dynamic nuclear polarisation - solid and cross effect fundamental theoretical research applied quantum non-equilibrium physics

4 Dynamics is more than statics... Non-interacting system Kinetically constrained system - Spins flip independently - Spins flip only if their left neighbour is excited Different dynamics Stationary state is the same Idealized models of glasses (FA, East)

5 Soft-matter physics with cold atoms Are there actual systems with manifest kinetic contraints? Cold gases of interacting excited (Rydberg) atoms Palaiseau group Science 354, 1021 (2016) Slow/glassy relaxation - emergence of new timescales - transient phenomena metastability - non-equilibrium stationary states Collective dynamics - nucleation, aggregation, growth - Non-equilibrium phase transitions Quantum effects - degree of quantumness is controllable

6 radial density Atoms in Rydberg states Energy level spectrum n+1 n ns n-1 Core + Rubidium 39s nm quantum defect: (l>4) 0 r

7 Atoms in Rydberg states - hydrogen-like - simple level structure - long lifetime ~ n ( 100 µs) - large displacement between charges Rydberg atoms s-states interact via van-der-waals interaction - scaling analysis shows: C 6 n 11!!!!! - for typical n-values (n=40 80) the interaction is 10 orders of magnitudes stronger than between ground state atoms (MHz-GHz over mm)

8 Recent experiments Strong correlations and crystallisation Bloch group, Science 347, 1455 (2015) Quantum gates Saffman group, PRL 104, (2010) Interacting photons Lukin group, Nature 488, 7409 (2012) Phase transitions and optical bistability Adams group, PRL 111, (2013)

9 From noise to kinetic constraints

10 Rydberg states Rydberg atoms as (pseudo)spins Energy level spectrum n+1 n ns n-1 Hamiltonian Excitation laser Rabi frequency Detuning Ground state

11 Quantum many-body dynamics - Spin ½ approximation: =ground state, =Rydberg state - dynamics is described by a Lindblad Master equation Hamiltonian (atoms at positions r k ) Jump operators dephasing γ Rabi frequency detuning interaction van-der-waals interaction decay G

12 Limit of strong noise - full problem is impossible to solve - strong noise limit permits drastic simplification quantum superposition noise Marcuzzi et al., J. Phys. A 47, (2014) only classical configurations remain: classical dynamics Kinetic constraint Flipping dynamics of non-interacting spins - non-trivial dynamics - trivial stationary state

13 Kinetic constraints/facilitation Resonant excitation Constraint function Off-resonant excitation (detuning ) excited atom blockaded/slow free/fast r excited atom resonant atom r Interaction parameter (,,blockade length ) Facilitation radius Experiments: Stuttgart, Pisa, Heidelberg, Ann-Arbour

14 Number of excitations Kinetic constraints are real Pisa experiment (Morsch group) PRA 93, (R) (2016) resonant Magneto-Optical Trap resonant facilitation facilitation Jochim group, Heidelberg ion counter always off-resonant excitation laser atomic cloud time always off-resonant

15 Collective phenomena and non-equilibrium phase transitions

16 A non-equilibrium phase transition The contact process Local dynamical rules: Unique absorbing state (no active sites) Γ λ DECAY BRANCHING

17 A non-equilibrium phase transition The contact process Local dynamical rules: Unique absorbing state (no active sites) Γ λ density of active sites DECAY INACTIVE PHASE ACTIVE PHASE BRANCHING - continuous phase transition (directed percolation universality class)

18 Non-equilibrium phase transition Why is this interesting? M Marcuzzi et al., NJP 17, (2015) - simplest non-equilibrium universality class - few clean realisations: 2D [Takeuchi et al. PRL 99, (2007)] 1D [Shi et al. Nat. Phys. 12, 254 (2016)] Rydberg non-equilibrium phase transition? - branching (facilitated excitation) λ - decay (radiative decay) Γ - unique absorbing state does not exist, due to Can one observe signatures of this phase transition in experiment?

19 Experimental results collaboration with Morsch group (Pisa) excitation laser Ω quasi one-dimensional disordered cloud ion counter protocol phase diagram - excite Rydberg atoms off-resonantly (detuning D) for a certain time (ideally reach stationary state) - apply electric field pulse - measure number of ions absorbing phase active phase number of ions n closer look at 10 MHz data

20 Experimental results closer look at 10 MHz data Gutierrez et al., PRA 96, (R) (2017) number of excitations fluctuations scaling Ω c 82.4 khz static exponent: β 0.31 ± data suggests (smoothed out) continuous order phase transition - compatible DP universality (static exponent: b=0.27) - lots of caveats (disorder, motion)

21 Quantum vs. classical fluctuations so far effective classical model Coherent excitation and interaction Decay work with M. Buchhold, S. Diehl (Cologne) Dephasing γ - remove dephasing to enter the quantum regime Model Hamiltonian,Quantum kinetic constraint quantum branching

22 Quantum vs. classical fluctuations Mean field treatment (,equation of state ) n stable solution - transition present also in quantum case and is of,,1 st order Numerics (12 sites in 1D) -,steady state distribution function absorbing state Ω/γ P(n) Ω/γ = 8 - bimodal distribution suggests 1 st order transition

23 quantum Quantum vs. classical fluctuations - what if quantum and classical branching compete? (Mean field) phase diagram First order transition in limit where quantum processes dominate Continuous transition (directed percolation) in classical limit classical Field-theoretical study presented in Phys. Rev. Lett. 116, (2016) Phys. Rev. B 95, (2017)

24 immunisation Quantum epidemics Elementary dynamics Perez-Espigares et al., PRL 119, (2017) - three states: healthy, immune and infected infection Implementation with Rydbergs - classical limit: general epidemic process infected - there is a manifold of absorbing states which the process reaches eventually - order parameter: number of immune sites - continuous transition in the dynamic percolation universality class healthy immune

25 Quantum epidemics - Rydberg gases allow to implement classical and quantum versions of an epidemic spreading process Classical limit Quantum limit - achieved with strong noise - continuous transition in dynamic percolation universality class - sequence of discontinuous jumps - first order transitions? - problem: calculation is (inhomogeneous) mean-field

26 Hyperpolarisation - Dynamic Nuclear Polarisation

27 Dynamic Nuclear Polarisation Magnetic Resonance Imaging - sensitivity depends on polarisation of nuclei - strong magnetic fields required Thermal equilibrium: p=10-6 at 300K and B=7 T brute force: 0.1 at 0.01K and B=14 T Out of equilibrium: at 1K and B=3-4 T Dynamical Nuclear Polarisation (solid effect) Mechanism: - Paramagnetic centres (electrons) are driven by microwave radiation - Polarisation is transferred to nuclei - Nuclear polarisation spreads (diffusion)

28 Hyperpolarisation Challenges for theory - understanding of the role of diffusion - simulation of large scale systems - optimisation of Dynamical Nuclear Polarisation solid: exact dashed: effective Solution - employ,rydberg gas methodology - analytical forms for diffusion rates - reduction of quantum many-body dynamics to classical kinetically constrained spin system,quantum,classical A. Karabanov, D. Wisniewski, IL, W. Kockenberger, PRL 115, (2015) Journal of Magnetic Resonance 264, 30 (2016)

29 Dynamic Nuclear Polarisation Simulation of large spin ensembles possible - Example: C spins coupled to a single electron electron Polarization build-up A. Karabanov, D. Wisniewski, IL, W. Kockenberger, PRL 115, (2015)

30 Beyond the solid effect Cross effect - two interacting electrons - mapping on effectively classical model works also here - three-body-dissipation accelerates build up Karabanov et al., arxiv: electrons nuclei Future - systematic optimisation of DNP (e.g. through multi-frequency fields) - design strategies DNP agents - competing cross and solid effect Bis-TEMPO biradical

31 Summary Rydberg soft matter M.M. Valado et al., PRA 93, (R) (2016) R. Gutierrez et al., PRA 96, (R) (2017) Non-equilibrium phase transition M. Marcuzzi et al., NJP 17, (2015) M. Marcuzzi et al., PRL 116, (2016) M. Buchhold et al., PRB 95, (2017) C. Espigares et al., PRL 119, (2017) Non-equilibrium transport ( ) Disordered systems and localization phenomena [PRL 118, (2017)] Rydberg ions [PRX 7, (2017)] Quantum generalisations of neural networks ( ) Applications in NMR A. Karabanov et al., PRL 115, (2015) D. Wisniewski et al., J. Mag. Res. 264, 30 (2016) A. Karabanov et al., PRL 119, (2017)