BEC 5 — Quantum Simulation with Lithium 7

Check out BEC5 lab website!

BEC 5 is the ⁷Li lab in the Ketterle group at MIT. We study ultracold bosons in optical lattices. The field
of cold atoms in optical lattices is inspired by the possibility to simulate the behavior of electrons in crystals
in a clean and controlled way. The atoms feel the dipole potential of the laser beams just as electrons feel
the ionic potential in a crystal. A ⁷Li system is advantageous because its Feshbach resonances allow us to
control the interactions between the atoms and the light mass of Li makes the dynamics faster. We use
two hyperfine states modeling spin up and spin down to study magnetic ordering at low temperatures
(Quantum Magnetism). The proximity in the phase diagram of the quantum antiferromagnets to the
superconducting state of high-temperature superconductors makes the study of magnetic ordering be
of major interest. With the ability to switch interactions from attractive to repulsive, our system can favor
antiferromagnetic ordering with bosons. Our system can simulate both spin 1/2 and spin 1, making it
possible to explore different exotic phases and the quantum phase transitions between them. 

We have recently investigated novel “phantom helix states” of 1D Heisenberg magnets and dynamics
of spin transport in far out-of-equilibrium states (see Research). We have made progress on preparing 
the many-body ground state of the Heisenberg model (manuscript accepted in 2023). We are now
upgrading our machine to incorporate single-site resolution with a high-NA microscope

Phantom helix states in Heisenberg quantum magnets

Jepsen, P.N., Lee, Y.K., Lin, H. et al. Long-lived phantom helix states in Heisenberg quantum magnets. Nat. Phys. 18, 899–904 (2022).

You can find an article on Phys.org summarizing our work here.

Quantum magnetism underlies many of the technologies we use today, including memory storage devices,
and is thus of fundamental interest. To model quantum magnetism, one can depict each elementary particle
as carrying a spin which can point in different directions. In this context, two nearby spins can exchange their
relative orientations via an intermediate state with both particles in the same place. 

This idea is captured by a simple textbook model called the Heisenberg spin model, which can
be realized in one dimension (i.e., a chain) in our experimental platform using ultracold atoms. 

Generically if we prepare a simple pattern of spins, say all spins aligned, then over time the pattern will
thermalize to a random mixture of spins pointing in all different directions and lose the information about
the initial state. These phantom helix states are special because they are protected against thermalization.

In non-integrable systems (e.g. in higher dimensions or with long-range interactions), phantom helix states
are actually quantum many-body scars, which are under intense investigation by the quantum community.
The XXZ Heisenberg model is one of the simplest many-body systems that can be realized that can also support scars.

Spin Transport in a Tunable Heisenberg Model

Jepsen, P.N., Amato-Grill, J., Dimitrova, I. et al. Spin transport in a tunable Heisenberg model realized with ultracold atoms. 
Nature 588, 403–407 (2020).

Simple spin physics captures the properties of many systems such as magnetic materials, high-T_c 
superconductors, systems with gauge fields, and more. Creating a versatile platform to study and
compare these models has been a long-standing goal in the field of ultracold atoms. To that end,
our lab has recently implemented the Heisenberg XXZ model with tunable interactions.

Nearest-neighbor couplings are mediated by superexchange (see below). We control the ratio
between the transverse coupling (J_xy) and longitudinal coupling (J_z), the “anisotropy,” by tuning
an applied magnetic field through Feshbach resonances between the two lowest hyperfine
states at high magnetic fields. Thus, we can explore the dynamics of spin transport throughout
a broad range of anisotropies.

We prepare a far out-of-equilibrium initial state, a “spin helix.” and find that the characteristic time
for spin transport scales as a power-law with the inverse of the wave vector Q = (2π / λ) of the helix.
In other words, τ ~ Q^-α. While scalings of ballistic-like transport (α = 1) and diffusive-like transport
(α = 2) had been predicted by theory, we unexpectedly discovered that the exponent α also varies
smoothly with anisotropy between 1 and 2 (super-diffusive transport), and even above 2 (sub-diffusive transport).

Enhanced Superexchange in a Tilted Lattice

Dimitrova, I., Jepsen, N., Buyskikh, A., Venegas-Gomez, A., Amato-Grill, J., Daley, A., & Ketterle, W. (2020). Enhanced Superexchange
in a Tilted Mott Insulator. Phys. Rev. Lett., 124(4), 43204.

When a tilt is added to the Mott insulator, first-order tunneling (at t) is suppressed, while second-order
tunneling (superexchange, at t²/U) persists. This separation between mass and entropy transport (at t)
and spin dynamics at t²/U has several new features for studying spin physics. (i) Arbitrary initial density
distributions can be used because the tilt can freeze them in. (ii) The Mott insulator-to-superfluid transition
can be suppressed, so that spin dynamics can be studied at lower lattice depths, where the dynamics are faster.
(iii) The parameters of the spin Hamiltonian can be tuned with the tilt. (iv) Defects, such as holes and doublons,
are made immobile by the tilt, enabling the study of pure spin dynamics.

Quantum Magnetism

We use the lowest two hyperfine states of Li 7 at high magnetic field to realize the 2-component
Bose-Hubbard model. We are interested in studying phenomena in Quantum Magnetism: the ordered
phases which arise when the dominant interaction between particles on a lattice is superexchange.
In particular, the 2-component Bose Hubbard Hamiltonian can be directly mapped onto the Heisenberg
spin Hamiltonian. In the context of the Bose Hubbard model, superexchange is a second-order tunneling
process, characterized by a matrix element “t²/U.” Here “t” is the hopping and “U” is the on-site interaction.
The phase diagram of this Hamiltonian includes ferromagnetic and anti-ferromagnetic phases aligned either
with the quantization axis “z” or with a line in the “xy”-plane. The main limitations so far for observing the full
phase diagram of this model have been the slow rate of the superexchange process compared to the lifetimes
of cold atoms in optical lattices and the very low critical temperatures required for superexchange to be the
dominant interactions. Li 7 promises to make improvements on both fronts. Its light mass leads to faster tunneling,
compared to other atoms, such as Rb, commonly used in Quantum Simulation experiments, so “t²/U” is large.
In addition, the critical temperature for magnetic ordering is also on the order of “t²/U,” so it can be reached
more easily with Li.

Interaction Spectroscopy

Amato-Grill, J., Jepsen, N., Dimitrova, I., Lunden, W., & Ketterle, W. (2019). Interaction spectroscopy of a two-component
Mott insulator. Physical Review A, 99(3), 1–5.

We would like to realize a Spin 1 model with the lowest two hyperfine states of Li 7 by going into
a Mott insulator with two atoms per site. We call the lowest two hyperfine states “a” and “b.” 

Interaction spectroscopy relies on the fact that the interactions between two atoms on a site depend on
the spin configuration of the two atoms. For example, the interactions between two “a” atoms, U_aa are
in principle different from the interactions between an “a” and a “b” atom, U_ab. The RF transition frequency
between two “a” atoms on a site and an “a” and a “b” atom on a site is shifted from the bare transition
between a single “a” and a single “b”atom on a site by the interaction difference U_ab-U_aa. We can flip
only one of the two atoms per site when the interaction differences are not degenerate, i.e. U_ab-U_aa 
is not equal to U_bb-U_ab. If the interaction differences degenerate, we can drive a transition from
“bb” all the way to “aa.”

We prepare a Mott insulator of “b” atoms and drive a spin-flip transition from “b” to “a.” We measure
the number of spin-flipped atoms (the number of “a” atoms) and we observe two peaks: One corresponding
to the transition of the n=1 shell of the Mott insulator at the bare transition frequency, and one of the n=2
shell at a frequency shifted by the interaction difference U_ab-U_aa. 

We use interaction spectroscopy to map out the interaction differences across the Feshbach resonances of Li 7.
In addition, we use amplitude modulation spectroscopy to measure the absolute value of the interactions.  

Finally, we find a point at which the interactions degenerate and drive a full Rabi oscillation between “bb” and “aa”

New Superradiant Regimes in a BEC

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.051603

We study superradiance with two non-interacting counterpropagating beams along the long axis of a BEC.
We find that there are two regimes in which the system behaves qualitatively differently. At low Rayleigh
scattering rates, the stimulated emission from the two beams cancel. At large Rayleigh scattering rates,
we see evidence of a formation of a different phase. Such a phase has been predicted in
[S. Ostermann, F. Piazza, and H. Ritsch, Phys. Rev. X 6, 021026 (2016)]. It consists of a stationary
density modulation and a standing optical wave. See our results here: https://arxiv.org/abs/1709.02028

Publications

Interaction spectroscopy of a
two-component Mott insulator

ArXiv: https://arxiv.org/abs/1809.06891
Jesse Amato-Grill, Niklas Jepsen, Ivana Dimitrova,
William Lunden, and Wolfgang Ketterle
Phys. Rev. A 99, 033612 (2019)

Observation of two-beam collective scattering phenomena in a Bose-Einstein condensate

ArXiv: https://arxiv.org/abs/1709.02028
Ivana Dimitrova, William Lunden, Jesse Amato-Grill,
Niklas Jepsen, Yichao Yu, Michael Messer, Thomas Rigaldo,
Graciana Puentes, David Weld, and Wolfgang Ketterle
Phys. Rev. A 96, 051603(R)  (2017)

Current Members

Graduate Students

Eunice (Yoo Kyung) Lee — eunlee@mit.edu

Hanzhen Li — linhz@mit.edu

Postdoctoral Associates

Vitaly Fedoseev — fedoseev@mit.edu

Principal Investigator

Wolfgang Ketterle — ketterle@mit.edu

Former Members

• Guoquing Wang — now a graduate student in Paola Cappellaro’s
  group at MIT
• Yichao Yu — now a graduate student at Harvard University,
  Ni group
• Alexander Keesling — now a graduate student at Harvard University,
  Lukin group 
• Michael Messer — now a graduate student at ETH, Tilman Esslinger’s group
• Thomas Rigaldo
• David Weld — now an assistant professor at UCSB
• Graciana Puentes —now Senior Researcher and Assistant Professor
  at CONICET and University of Buenos Aires – Permanent position