Explana'on of the Higgs par'cle

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4 Explana'on of the Higgs par'cle

5 Condensed ma7er physics: The Anderson- Higgs excita'on

6 Press release of Nature magazine

7 Unity of Physics laws fev pev nev µev mev ev kev MeV GeV TeV pk nk µk mk K Cold atoms experiments K room temperature LHC Higgs mode in ultracold atoms, 2012 Higgs mode of the standard model, 2012

8 Discovery of the Higgs par'cle at LHC is really important. It shows that the standard model of elementary par'cles really works If you accept idea of symmetry breaking in the standard model, the Higgs par'cle is really simple! Spontaneous symmetry breaking in Quantum Mechanics Goldstone modes Higgs mode

9 Spontaneous symmetry breaking

10 Spontaneous symmetry breaking Classical mechanics. Simple example g Gravity is pulling the mass down Spring k is pulling the mass up

11 Spontaneous symmetry breaking Classical mechanics. Simple example K<K crit K>K crit The system chooses one of the minima. This breaks the inversion symmetry

12 Classically either of the solutions is allowed

13 Quantum mechanical solution + For the even potential all eigenstates satisfy Ground state Eigenstates of the Hamiltonian are eigenstates of inversion symmetry operator

14 Symmetry Quantum mechanical system with Hamiltonian H Symmetry of the system described by the operator G [H,G]=0 Theorem: When operators H and G commute, We can diagonalize H and G simultaneously. Then the ground state of H should be an eigenstate of G. Spontaneous symmetry breaking: violation of the theorem

15 Spontaneous symmetry breaking In the limit of an infinite system an infinitesimal perturba'on is enough to cause the system to break the symmetry of H. The fact that symmetry breaking can happen is signaled by non- commuta'vity of limits

16 Theorem of Quantum Mechanics: When operators H and G commute, We can diagonalize H and G simultaneously. Then the ground state of H should be an eigenstate of G. Spontaneous symmetry breaking: in the thermodynamic limit (# of par'cles - > infinity) we can find ground states that do not obey this condi'on

17 Examples of Symmetry and symmetry breaking

18 Example. Transla'onal symmetry

19 Crystals: atoms are localized and the ground state is not an eigenstates of total momentum According to direct interpreta'on of the QM theorem, crystal ground state should have a well defined total momentum. It should have equal probability to be everywhere.

20 Example. Spin symmetry

21 Magnets: S 2 tot commutes with H. However classical magne'c states are not eigenstates of An'ferromagne'c state is not an eigenstate of S 2 tot From the an'ferromagne'c chain consider two spins only

22 Consider simple example of only two spins Eigenstates An'ferromagne'c state mixes eigenstates

23 Example. Superconduc'vity and superfluidity Conserved quan'ty: total number of par'cles N

24 Bose-Einstein Condensation (BEC) and Superfluidity BEC of non-interacting particles at T=0 BEC of interacting particles: macroscopic occupation of one state Finite temperature has similar effect

25 Bose-Einstein Condensation and spontaneous symmetry breaking Condensate wavefunction describes complex order parameter

26 Superfluidity of ultracold atoms in optical lattices

27 Atoms in optical lattices Theory: Jaksch et al. PRL (1998) Experiment: Kasevich et al., Science (2001); Greiner et al., Nature (2001); Phillips et al., J. Physics B (2002) Esslinger et al., PRL (2004); Ketterle et al., PRL (2006)

28 Bose Hubbard model M.P.A. Fisher et al., PRB (1989) D. Jaksch et al. PRL (1998) t U tunneling of atoms between neighboring wells repulsion of atoms sitting in the same well

29 Bose Hubbard model N=3 Mott M.P.A. Fisher et al., PRB40:546 (1989) N=2 Mott Superfluid N=1 Mott 0 Superfluid phase Weak interactions Mott insulator phase Strong interactions

30 Superfuid state

31 Mott insulating state

32 Superfluid to insulator transition in an optical lattice M. Greiner et al., Nature 415 (2002) Mott insulator Superfluid t/u

33 Single atom resolution in optical lattices Bakr et al., Science 2010 density x y

34 Excitations = Collective modes

35 Collec've modes of strongly interac'ng superfluid bosons Order parameter Breaks U(1) symmetry Phase (Goldstone) mode = gapless Bogoliubov mode Gapped amplitude mode (Higgs mode)

36 Excita'ons of the Bose Hubbard model 2 n=3 Mo7 Superfluid 2 n=2 Mo7 1 n=1 Mo7 Mo7 Superfluid 0 Sodening of the amplitude mode is the defining characteris'c of the second order Quantum Phase Transi'on

37 Is there a Higgs resonance 2d? D. Podolsky et al., arxiv: Earlier work: S. Sachdev (1999), W. Zwerger (2004)

38 Exci'ng the amplitude mode Deposi'ng energy into the system: like shining light on atoms to probe electron energy levels

39 Exci'ng the amplitude mode M. Endres et al., Nature 487:454 (2012) n=1 Mo7 n=1 Mo7 n=1 Mo7

40 Experiments: full spectrum M. Endres et al., Nature 487:454 (2012)

41 Absorp'on spectra. Theory (1x1 calcula'ons) disappearing amplitude mode Breathing mode details at the QCP spectrum remains gapped due to trap

42 Higgs Drum Modes 1x1 calcula'on, 20 oscilla'ons E abs rescaled so peak heights coincide Similar to Higgs mode in compac'fied dimensions

43 Quantum simulations with ultracold atoms

44 Solving fundamental problems with quantum technology Open challenges in physical sciences Understand and design quantum materials one of the biggest challenges in Physics in the 21 century High temperature superconduc'vity (electricity) Magne'sm (data storage) 10-20% of electric power is lost in transmission. This problem can be solved by creating lossless transmission lines from high temperature superconductors

45 Why we can not solve these problems with conven'onal computers Example: Electrons on a lamce. S System underlying many solid state and materials problems. Magnets, High Temperature Superconductors, Spintronics,

46 Each doubling allows for one more spin ½ only

47 Modeling: from airplanes to wind- tunnels Quantum simula'ons: understanding high Tc superconductors using ar'ficial quantum systems

48 Quantum simulations with ultracold atoms Atoms in optical lattice Antiferromagnetic and superconducting Tc of the order of 100 K Antiferromagnetism and pairing at nano Kelvin temperatures Same microscopic model

49 Summary Experiments with ultracold atoms provide a new perspec've on the physics of strongly correlated many- body systems. Quantum noise is a powerful tool for analyzing many body states of ultracold atoms Thanks to: