Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals -...

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Ultra Quantum Matter Simons Collaboration Kickoff Meeting Ashvin Vishwanath Harvard University

Transcript of Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals -...

Page 1: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Ultra Quantum Matter Simons Collaboration Kickoff Meeting

Ashvin VishwanathHarvard University

Page 2: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Simons Collaboration on Ultra Quantum Matter

What is “Ultra-Quantum”?

Why does it matter?

Why now ?

Page 3: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Highly Entangled Quantum Matter

Solid - Classical order parameter ρ(q) - density

vs.

Leon Balents

“Ultra” Quantum Matter

Quantum Hall States: Highly entangled quantum states

B

Page 4: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Non-local Quantum Entanglement

-2γ = SB +SABC −SBC −SAB

LevinandWen

Quantum Hall state γ>0

Entanglement - EPR Pair

Page 5: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Classical orders vs Ultra-quantum Matter

• Crystals - classify all patterns of symmetry braking (230 space groups)

• Probe - using X-ray scattering

• All 230 space groups realized in nature.

• Classify gapped/gapless highly entangled quantum ground states.

• Novel probes needed

• Realize or engineer in synthetic systems.

Page 6: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Why - ultra quantum matter?• Deep connections between quantum field theory,

condensed matter and quantum information.

• Highly entangled quantum states closely related to quantum information processing.

• Quantum Error Correction & Topological Order

• Fractons & robust quantum memory

• Materials with entirely new properties? (eg. Higher Tc superconductors?)

Page 7: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Why now?

• Remarkable relations derived between apparently distinct phenomena.

• Rapid improvements in probing and creating synthetic quantum systems.

“quantum”

dualities

quantum spin liquids

Topological insulators

Quantum Hall Effect

non-Landau deconfined criticaility

2

fluctuations or restore its quantum purity. In such a way,the spin’s entanglement with another spin creates localentropy, called entanglement entropy. Entanglement en-tropy is not a phenomenon restricted to spins, but existsin all quantum systems that exhibit entanglement. Andwhile probing entanglement is a notoriously di�cult ex-perimental problem, this loss of local purity, or, equiva-lently, the development of local entropy, establishes thepresence of entanglement when it can be shown that thefull quantum state is pure.

In this work, we directly observe a globally pure quan-tum state dynamically lose local purity to entanglement,and in parallel become locally thermal. Recent exper-iments have demonstrated analogies between classicalchaotic dynamics and the role of entanglement in few-qubit spin systems [14], as well as the dynamics of ther-malization within an ion system [15]. Furthermore, stud-ies of bulk gases have shown the emergence of thermalensembles and the e↵ects of conserved quantities in iso-lated quantum systems through macroscopic observablesand correlation functions [16–19]. We are able to di-rectly measure the global purity as thermalization occursthrough single-particle resolved quantum many-body in-terference. In turn, we can observe microscopically therole of entanglement in producing local entropy in a ther-malizing system of itinerant particles, which is paradig-matic of the systems studied in statistical mechanics.

In such studies, we will explore the equivalence be-tween the entanglement entropy we measure and the ex-pected thermal entropy of an ensemble [11, 12]. We fur-ther address how this equivalence is linked to the Eigen-state Thermalization Hypothesis (ETH), which providesan explanation for thermalization in closed quantum sys-tems [6, 7, 9, 10]. ETH is typically framed in termsof the small variation of observables (expectation val-ues) associated with eigenstates close in energy [6, 7, 10],but the role of entanglement in these eigenstates isparamount [12]. Indeed, fundamentally, ETH implies anequivalence of the local reduced density matrix of a singleexcited energy eigenstate and the local reduced densitymatrix of a globally thermal state [20], an equivalencewhich is made possible only by entanglement and theimpurity it produces locally within a global pure state.The equivalence between these two seemingly distinctsystems, the subsystems of a quantum pure state anda thermal ensemble, ensures thermalization of most ob-servable quantities after a quantum quench. Throughparallel measurements of the entanglement entropy andlocal observables within a many-body Bose-Hubbard sys-tem, we are able to experimentally study this equivalenceat the heart of quantum thermalization.

EXPERIMENTAL PROTOCOL

For our experiments, we utilize a Bose-Einstein con-densate of 87Rb atoms loaded into a two-dimensional op-tical lattice that lies at the focus of a high resolution

Quench

1-11-1-1-1

Expansion to Measure Local and Global Purity

-111-111

Expansion to Measure Local Occupation Number

102210

210102

~ 50

Site

s

~ 50

Site

s

Mott insulatorEven Odd

680

nm

Initialize Many-bodyinterference

45 E

r

6 E

r

Global thermal state purity

Locally thermalLocally pure Globally pure

On-site Statistics

Particle number0time after quench (ms)

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

Entropy: -Log(T

r[ρ 2])

100

10-2 4.6

2.3

0

10 20

A

B

C

y

x

Initial state

quench

Pur

ity: T

r[ρ2 ]

10-1

P(n

)

0

0.2

0.4

0.6

0.8

1

P(n

)

Particle number0 1 2 3 4 5 6

On-site Statistics Many-body purity

t=0 ms t=16 ms

6 site system 6 site system

FIG. 2. Experimental sequence (A) Using tailored opticalpotentials superimposed on an optical lattice, we determin-istically prepare two copies of a six-site Bose-Hubbard sys-tem, where each lattice site is initialized with a single atom.We enable tunneling in the x-direction and obtain either theground state (adiabatic melt) or a highly excited state (sud-den quench) in each six-site copy. After a variable evolutiontime, we freeze the evolution and characterize the final quan-tum state by either acquiring number statistics or the localand global purity. (B) We show site-resolved number statis-tics of the initial distribution (first panel, strongly peakedabout one atom with vanishing fluctuations), or at later times(second panel) to which we compare the predictions of acanonical thermal ensemble of the same average energy as thequenched quantum state (J/(2⇡) = 66 Hz, U/(2⇡) = 103 Hz).Alternatively, we can measure the global many-body purity,and observe a static, high purity. This is in stark contrast tothe vanishing global purity of the canonical thermal ensemble,yet this same ensemble accurately describes the local numberdistribution we observe. (C) To measure the atom numberlocally, we allow the atoms to expand in half-tubes along they-direction, while pinning the atoms along x. In separate ex-periments, we apply a many-body beam splitter by allowingthe atoms in each column to tunnel in a projected double-wellpotential. The resulting atom number parity, even or odd, oneach site encodes the global and local purity.

imaging system [21, 22]. The system is described by theBose-Hubbard Hamiltonian,

H = �(JxX

x,y

a†x,yax+1,y + Jy

X

x,y

a†x,yax,y+1 + h.c.)

+U

2

X

x,y

nx,y(nx,y � 1), (1)

where a†x,y, ax,y, and nx,y = a†x,yax,y are the bosonic cre-

ation, annihilation, and number operators at the site lo-

Measuring entanglement Greiner lab. Proposed by Zoller et al.

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A remarkable relation

• Close relation between half filled Landau level and the surface of topological insulators.

[Gapped <->Gapless; 3D<->2D]

• Fermion-Fermion electric-magnetic duality. (Son, Chong Wang & Senthil, Metlitski and AV, Seiberg, Witten, Karch &Tong, Kachru)

Topological Insulators Fu, Kane, Mele, Moore, Balents, Roy,

Qi, Hughes, Zhang

Kx#

Ky#

Half filled Landau level Halperin Lee Read

Page 9: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Michael Levin Chicago

Xie Chen Caltech

Max Metlitski MIT

Lukasz Fidkowski UW Seattle

 2020 New Horizons in Physics Prize  

For incisive contributions to the understanding of topological states of matter

and the relationships between them.

Page 10: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

Simons Collaboration Team

Here is a photograph of McGreevy

Xie Chen

Michael Levin

Victor Gurarie

Shamit Kachru

Xiao-Gang Wen

Victor Galitski

Michael Hermele

T. Senthil

Matthew FisherPeter Zoller

Subir SachdevJohn McGreevy

Dam Thanh Son

Leon Balents

Nati Seiberg

Andreas KarchAshvin Vishwanath

Page 11: Ultra Quantum Matter - Harvard UniversityClassical orders vs Ultra-quantum Matter • Crystals - classify all patterns of symmetry braking (230 space groups) • Probe - using X-ray

9:45 – 10:30 Overview of Fracton UQM, and "Entanglement renormalization of fractonic gauge theories”

Xie Chen

10:30 – 11:00 “Higher symmetries, p-string condensation and fractons” Michael Hermele

11:00 – 11:25 Break Library

11:25 – 11:55 "Mimicking the edge of 2d topological insulators and superconductors in a 1d lattice model"

Max Metlitski