Dynamical phase transition and prethermalization. Mobile magnetic impurity in Fermi superfluids

Dynamical phase transition and prethermalization Pietro Smacchia, Alessandro Silva (SISSA, Trieste) Dima Abanin (Perimeter Institute, Waterloo) Michael Knap, Eugene Demler (Harvard) Mobile magnetic impurity in Fermi superfluids Sarang Goplalakrishnan, Eugene Demler (Harvard)

Dynamical phase transition and prethermalization

Prethermalization Heavy ions collisions QCD We observe irreversibility and approximate thermalization. At large time the system approaches stationary solution in the vicinity of, but not identical to, thermal equilibrium. The ensemble therefore retains some memory beyond the conserved total energy This holds for interacting systems and in the large volume limit. Prethermalization in ultracold atoms, theory: Eckstein et al. (2009); Moeckel et al. (2010), L. Mathey et al. (2010), R. Barnett et al.(2010)

Prethermalization in 1 dimensional system Probing prethermolization in atomchipexperiments Gring et al., Science (2012) Initial T=120 nk (blue line). After 27.5 ms identical to thermal system at T= 15 nk At all lengthscales In all correlation functions

Quench and wait Ultracold bosons in optical lattices Quantum quench from Mott insulator to superfluid + wait:

Dynamical Phase transition We look at the long time limit of the system. What is the nature of the stationary state? Is it thermal? Does it become superfluid? Earlier work: Eckstein et al., PRL 103:056403 (2009) Schiro, Fabrizio, PRL 105: 076401 (2010) Sciola, Biroli, PRL 105:220401 (2010) Gambassi, Calabrese, EPL 95:66007 (2011) Sciola, Birolli, arxiv:1211.2572

Experimental probes using quantum microscope Statistics of defects defect densi es and their higher moments (fluctuations, skewness,...) local defects density d (lower case d): average moments cumulants global defects D (upper case D): average moments cumulants (same as before)

Large N model Dynamical phase transition from Mott to Superfluid at quan zed densi es O(2) field theory large N limit: interaction factorizes decoupled harmonic oscillators with time dependent mass (to be determined self consistently)

Large N model Stationary point at long times can be found (without crossing the dynamical phase transition) For d>2 there is a transition when r*=0

Critical properties of dynamical phase transition

Experimental signatures of dynamical phase transition Use field theory to calculate the number of excitations in the basis of the Hamiltonian before the quench. This corresponds to the number of defects in the system Average number of defects saturates at long wait times with or without crossing the DPT. Nothing special at the dynamical phase transition. (Equilibration?) The variance in the number of defects shows very different behavior before and after crossing the dynamical phase transition. without crossing DPT after crossing DPT

Defect counting in O(N) model model reduces to a set of harmonic oscillators with time dependent masses initial state has no defects: ground state of quench the mass of the oscillators wave func on is squeezed state from we calculate density: fluctuations:

Defect counting in O(N) model Moment generating function Individual moments

Prethermalization Divergence in the variance of the number of defects demonstrates prethermalization (introduced by Wetterich et al., see e.g. hep-th/0403234). The system has anomalous occupation of the low energy modes

Prethermalization Ratio of the cumulants Precursors of higher moments diverging at DPT C 1 /C 2 C 2 /C 3 Dynamical phase transition at r*=0 'Mott'

Is this prethermalization real? exact dynamics in 1D with DMRG local defects: C 1 C 2

Steady state cumulants of global defects D (as in field theory) approach quickly the thermal value Defect statistics

Steady state cumulants of local defects approach quickly the thermal value (~ 2 3 1/J 2 times) (thermal value: solid line; temporal average: symbols)

Relaxation in 4 theory beyond large N Berges et al., Nucl. Phys. B 727:244 (2005)

Open questions Does a prethermalized regime exist in higher dimension? this is hard (impossible?) to answer theoretically experimental study would give insight in the validity of O(N) for dynamics of bosons thermal values can be easily obtained by QMC in higher dimension 1D: O(N) and DMRG give even qualitative difference for cumulant ratio: Mott Mott

Open questions Does a prethermalized regime exist in higher dimension? this is difficult (impossible?) to answer theoretically experimental study would give insight in the validity of O(N) for dynamics of bosons thermal values can be easily obtained by QMC in higher dimension 1D: agreement improves when going to larger filling (particle hole symmetry) Mott Mott slight decrease?

Mobile magnetic impurities in Fermi superfluids

Impurities in solid state systems

Bound states on magnetic impurities in superconductors

Bound states on magnetic impurities in superconductors Yu, Acta Phys. Sin. 21, 75 (1965) Shiba, Prof. Theor. Phys. 40, 435 (1968). Rusinov, Sov. Phys. JETP Lett. 9, 85 (1969) Salkola, Balatsky, Schrieffer, PRB 55:12648 (1997)

Local density of states near Science 275:1767 (1997)

Parity changing transition Salkola, Balatsky, Schrieffer, PRB 55:12648 (1997) Analogous to Kondo singlet formation

Possible realization: Cs impurities in Li fermionic condensate e.g. Chen Chin s group

Bound state of Bogoliubov quasiparticle and impurity atom

Sketch of the wavefunction

Bound state energy

Weak interaction: parity transition Shiba Kondo molecule

Strong interaction: global minimum Shiba Kondo molecule

Exotic molecule

Detection via RF

Exotic many-body phases? Reminiscent of electrons with spin-orbit coupling Interaction between two Shiba states: Yao et al., 13092633 in 2D and contact interaction, ground state: breaks rotational symmetry. Wigner crystal or nematic. Berg, Rudner, Kivelson (2012) For contact interaction Wigner crystal with aspect ratio has energy per particle parametrically better than uniform phase

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