dipolar physics in latticesbqmc.upc.edu/pdfs/doc917.pdfdipolar physics in lattices...

Dipolar physics in latticesQuantum magnetism and exotic quantum phases with molecules

Jordi Mur-Petit

Department of PhysicsClarendon Laboratory

Dipolar physics in lattices [email protected] physics in lattices [email protected] UNIVERSITY OF OXFORD

Outline● Intro: Our group in Oxford

● Quantum impurities as probes

● Revealing hidden charges

● Many-body physics with polar molecules● Great theoretical expectations● Recent experimental results● Our research plans


Quantum Systems EngineeringDieter Jaksch

Jordi Mur-PetitMartin Kiffner

Frank SchlawinAlex Glaetzle

Michael LubaschJaewoo Joo

Karsten LeonhardtBerislav Buca

Jon CoulthardAnastasia Dietrich

Paolo RossonHongmin Gao

Joey TindallNikita Gourianov

www.TNTgo.org


Q. Systems Engineering group Quantum Materials Control (ERC Synergy) NQIT (UK Q-Hub)

TNT library Q. Probes of Complex Systems (QuProCS – EU FET-Proactive)

● 6+1 partners


Quantum impurities

Impurity in quantum system

- Spin-boson model

- Polaron’ problem‛

- Quantum probe

Recati et al., PRL 2005

Catani et al., 2012

Fukuhara et al., 2013


Multi-rf trap for Rb-85 & Rb-87

Rb-87

Rb-85

E. Bentine,..., JMP, Ch. Foot, J. Phys. B 40, 094002 (2017)


Q. probing: Correlations

M. Streif, A. Buchleitner, D. Jaksch & JMP, PRA 94, 053634 (2016)

(Bose-Hubbard)

(= qubits)

Bose-Hubbard model: Two phases

- U/J << 1: superfluid

- U/J >> 1: Mott insulator

Rb-87: system’‛

Rb-85: quantum probes


Q. probing: Correlations

(Bose-Hubbard)

(= qubits)



Correlations: SF-MI transition

TheoryTheoryTheory

Bogoliubov Theory

TNT calculations


On-siteg(2)(0)

NN:g(2)(a)

NNN:g(2)(2a)


Fluctuations?Thermodynamic Laws (1824-)

Image: Wikipedia

[Photo by user Chianti, Wikipedia]


Fluctuations? Bounded!

Collin et al., Nature (2005)

Fluctuation Relations (1993-)

Crooks relation

Constrain P(w):

Jarzynski equality

Thermodynamic Laws (1824-)

Image: Wikipedia


Quantum Fluctuation Relations

Quantum Jarzynski equality (QJE)

Tasaki-Crooks relation (TCR)

QJE: Tasaki (2000), Kurchan (2000), Yukawa (2000), Mukamel (2003), DeRoeck & Maes (2004); TCR: Tasaki (2000), Monnai (2005)

{BW:

FW:


Quantum Fluctuation RelationsInitial state of system?Thermal equilibrium = Gibbs :

{BW:

FW:


Quantum Fluctuation RelationsInitial state of system?Thermal equilibrium = Gibbs :

If system has conserved quantitiesThermal equilibrium = GGE :

Kinoshita et al.Nature (2006)


Generalised QJE

Generalised TCR

Generalised QFRs

JMP, A. Relaño, R.A. Molina, D. Jaksch, arXiv:1711.00871

{BW:

FW:


Gen. TCR: Quenched Dicke model

JMP, A. Relaño, R.A. Molina, D. Jaksch, arXiv:1711.00871

Dipolar physics in latticesQuantum magnetism and exotic quantum phases with molecules

Jordi Mur-Petit

Department of PhysicsClarendon Laboratory


QSUM

DurhamSimon CornishJeremy Hutson

OxfordDieter JakschJMP

ImperialEd HindsMike TarbuttBen SauerAlex Clark

2017-2022£6.7M

www.qsum.org.uk


QSUM2017-2022£6.7M

“Our Vision is to achieve full quantum control of cold and ultracold molecules in order to advance the science of complex quantum systems and underpin new quantum technologies.”


1. Chemistry2. Fundamental tests (e.g., PT violation)3. Precision measurements: α, m

p/m

e

4. Q Info / Q Computation: use internal d.o.f. for qubit5. Quantum Simulation: Dipolar systems

● Long range & anisotropic interactions● Exotic phases● Permanent EDM, ‘easily’ controllable by ext. fields

Nat. Phys. 2, 341 (2006)>800 citations

Nat. Phys. 2, 341 (2006)

NJP 11, 055049 (2009)

Why cold molecules?


Without lattice: Crystallisation

Astrakharchik et al. PRL 98 060405 (2007); Büchler et al., id. 060404 (2007)

Dipoles in 2D: Polarised perpendicular to plane● Density-driven quantum phase transition solid-gas

(‘dipolar analogue of Wigner crystallisation’)

xy

zE


Crystallisation with a tilt

Macià et al. PRL 109 235307 (2012); PRA 90 061601(R) (2014)

Dipoles in 2D: Polarised to angle α w.r.t. normal to plane● For α > 0.6 rad (~35 º): collapse ● For α > 0.4 rad (~23 º): stripe phase (anisotropic)

Gas Stripe


Lattice: Q. magnetism (spin models)

Micheli et al. Nat. Phys. 2 341 (2006); André et al., ibid. 636 (2006).

Idea: Use lower rot. states (N=0,1) of 2Σ molecule as pseudo-spinCouple them with mw → non-zero EDM● v=0 states → longer lifetime (≈103s) than (optical) atomic systems● tuning mw freq & polarization → engineer interactions

π,σ±




2D

π,σ±





3D (2 x 2D layers)



Other exotic phases● Supersolids● Topological states:

● Büchler et al., PRL 98 060404 (2007)● André et al., Nat. Phys. 2, 626 (2006)

● Spin ice with (Ryd.) dipoles: Glaetzle et al., PRX 4 041037 (2014)● Spin glasses: Lechner & Zoller, PRL 111, 185306 (2013)● ...


Recent highlightsYan et al. [Jin & Ye], Nature 2013Coherent dipole-dipole dynamics in fermionic KRb in 3D lattice

Testing coherence:– No spin-echo, <1ms– Single pulse spin-echo– Multipulse sequence

Interaction effect:Coh. evolution of superposition of tworotational states

Inferred couplings:



Molony et al. [Cornish], PRL 2014Gregory et al. [Cornish], PRA 2016Coherent dynamics btw hfs states in bosonic RbCs – No latt. Accurate spectroscopy of trapping light effects



Molony et al. [Cornish], PRL 2014Gregory et al. [Cornish], PRA 2016Coherent dynamics btw hfs states in bosonic RbCs – No latt.Accurate spectroscopy of trapping light effects

Molecules with electric & magnetic dipole momentsCsYb (X 2Σ+) @ Durham/Imperial [Cornish, Rev. Sci. Instr. 2016]CaF (X 2Σ+) @ Imperial [Tarbutt/Hinds, Nature Phys. 2017]NaLi (a 3Σ+Π) @ MIT [Zwierlein/Ketterle/Jamieson, PRL 2017]


Challenges ahead● How cold do we need to be?

E.g.: Crystallisation




● (Quasi)2D: How tightly do we need to trap?




● (Quasi)2D: How tightly do we need to trap?

● How many internal states?


Our research plans● Support experiments

● Quenches in dipolar gases: α(t): Driving a dynamical QPT?

Mean-field approach → collaboration w/ Weizhu Bao (NUS)

● CsYb: electric & magn. dipole moments➢ Competing long-range interactions

→ exotic phases? (w/ or w/o hopping)➢ Analytical insights → Alex Glaetzle➢ Numerics: 2D, long-range, beyond

mean-field → TNT team

Eα

xy

z

[www.TNTgo.org]


Tensor Network TheoryWell grounded for 1D systems with short-range interactions

We’ve got an advanced numerical library for● ground state & finite temperature calculations● static & time-dependent processes

Need to advance & apply:● Efficient methods for 2D systems

Including long-range interactions

For particles with a potentially large number of internal states(rotational, hyperfine q. numbers)

www.TNTgo.org


Summary● Intro: Our group in Oxford

● Quantum impurities as probes

● Revealing hidden charges

● Many-body physics with polar molecules

M. Streif et al., PRA 94 053634 (2016)E. Bentine et al.,JPB 50 094002 (2017)

JMP et al., arXiv:1711.00871


Gràcies!Dieter Jaksch

Jordi Mur-PetitMartin Kiffner

Frank SchlawinAlex Glaetzle

Michael LubaschJaewoo Joo

Karsten LeonhardtBerislav Buca

Jon CoulthardAnastasia Dietrich

Paolo RossonHongmin Gao

Joey TindallNikita Gourianov

www.TNTgo.org

dipolar physics in latticesbqmc.upc.edu/pdfs/doc917.pdfdipolar physics in lattices...

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