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Ultra Quantum Matter Simons Collaboration Kickoff Meeting
Ashvin VishwanathHarvard University
Simons Collaboration on Ultra Quantum Matter
What is “Ultra-Quantum”?
Why does it matter?
Why now ?
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
Non-local Quantum Entanglement
-2γ = SB +SABC −SBC −SAB
LevinandWen
Quantum Hall state γ>0
Entanglement - EPR Pair
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.
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?)
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.
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
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.
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
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
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