New experiments using trapped one-dimensional gases — atoms cooled to the
coldest temperatures in the universe and confined so that they can only move
in a line — fit with the predictions of the recently developed theory of
“generalized hydrodynamics.” Quantum mechanics is necessary to describe the
novel properties of these gases. Achieving a better understanding of how
such systems with many particles evolve in time is a frontier of quantum
physics. The result could greatly simplify the study of quantum systems that
have been excited out of equilibrium. Besides its fundamental importance, it
could eventually inform the development of quantum-based technologies, which
include quantum computers and simulators, quantum communication, and quantum
sensors. A paper describing the experiments by a team led by Penn State
physicists appears Sept. 3 in the journal Science.

Even within classical physics, where the additional complexities of quantum
mechanics can be ignored, it is impossible to simulate the motion of all the
atoms in a moving fluid. To approximate these systems of particles,
physicists use hydrodynamics descriptions.

“The basic idea behind hydrodynamics is to forget about the atoms and
consider the fluid as a continuum,” said Marcos Rigol, professor of physics
at Penn State and one of the leaders of the research team. “To simulate the
fluid, one ends up writing coupled equations that result from imposing a few
constraints, such as the conservation of mass and energy. These are the same
types of equations solved, for example, to simulate how air flows when you
open windows to improve ventilation in a room.”

Matter becomes more complicated if quantum mechanics is involved, as is the
case when one wants to simulate quantum many-body systems that are out of
equilibrium.

“Quantum many-body systems — which are composed of many interacting
particles, such as atoms — are at the heart of atomic, nuclear, and particle
physics,” said David Weiss, distinguished professor of physics at Penn State
and one of the leaders of the research team. “It used to be that except in
extreme limits you couldn’t do a calculation to describe out-of-equilibrium,
quantum many-body systems. That recently changed.”

The change was motivated by the development of a theoretical framework known
as generalized hydrodynamics.

“The problem with those quantum many-body systems in one dimension is that
they have so many constraints on their motion that regular hydrodynamics
descriptions cannot be used,” said Rigol. “Generalized hydrodynamics was
developed to keep track of all those constraints.”

Until now, generalized hydrodynamics had only previously been experimentally
tested under conditions where the strength of interactions among particles
was weak.

“We set out to test the theory further, by looking at the dynamics of one
dimensional gases with a wide range of interaction strengths,” said Weiss.
“The experiments are extremely well controlled, so the results can be
precisely compared to the predictions of this theory.

The research team uses one dimensional gases of interacting atoms that are
initially confined in a very shallow trap in equilibrium. They then very
suddenly increase the depth of the trap by 100 times, which forces the
particles to collapse into the center of the trap, causing their collective
properties to change. Throughout the collapse, the team precisely measures
their properties, which they can then compare to the predictions of
generalized hydrodynamics.

“Our measurements matched the prediction of theory across dozens of trap
oscillations,” said Weiss. “There currently aren’t other ways to study
out-of-equilibrium quantum systems for long periods of time with reasonable
accuracy, especially with a lot of particles. Generalized hydrodynamics
allow us to do this for some systems like the one we tested, but how
generally applicable it is still needs to be determined.”

## Reference:

Neel Malvania, Yicheng Zhang, Yuan Le, Jerome Dubail, Marcos Rigol, David S.
Weiss. Generalized hydrodynamics in strongly interacting 1D Bose gases.
Science, 2021; 373 (6559): 1129
DOI: 10.1126/science.abf0147

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