Session D49: Precision Many-Body Physics I: Quantum matter

Quantum Register of Fermion Pairs and Crystallization of Quantum Hall states

I will discuss two recent quantum gas experiments at MIT: The demonstration of a quantum register made of fermion pairs and the crystallization of bosonic quantumHall states. The “glue” between these rather orthogonal topics is the harmonic oscillator that underlies these experiments. For the quantum register we observed long-lasting coherence of the relative and center-of-mass motion of fermion pairs, which may serve as a novel type of qubit. In the work on rotating quantum gases, we empoly a harmonic trap to perfectly cancel the centrifugal force in the rotating frame, so as to be able to observe the pure evolution of a bosonic quantum Hall state – a Landau gauge wavefunction – in “flat land” - under the sole influence of interactions and the effective magnetic field provided by the Coriolis effect. We observe that this wavefunction is unstable against crystallization, and show that the instability smoothly connects from the quantum regime to the classical description of a Kelvin-Helmholtz-like instability of counterflow.

[1] Thomas Hartke, Botond Oreg, Ningyuan Jia, Martin Zwierlein

Quantum Register of Fermion Pairs

Nature 601, 537–541 (2022)

[2] Biswaroop Mukherjee, Airlia Shaffer, Parth B. Patel, Zhenjie Yan, Cedric C. Wilson, Valentin Crépel, Richard J. Fletcher, Martin Zwierlein

Crystallization of Bosonic Quantum Hall States

Nature 601, 58–62 (2022)   

Impacts of random filling on spin squeezing via Rydberg dressing in optical clocks

Spin squeezing via Rydberg dressing in an optical lattice can increase the accuracy of atomic clocks. The squeezing is generated when a sequence of Zeeman and long-range Ising-like interactions is applied to an array of Rydberg atoms trapped in an optical lattice. We analyze the effect of random fractional filling of the optical lattice on the spin squeezing characteristics. We compare the achievable clock stability in different lattice geometries, including unity-filled tweezer clock arrays and fractionally filled lattice clocks. We provide approximate analytical expressions and fitting functions to aid in the experimental implementation of Rydberg-dressed spin squeezing. We demonstrate that spin squeezing via Rydberg dressing in one-, two-, and three-dimensional optical lattices can significantly improve stability in the presence of random fractional filling.   

The quantum phases of square lattice Rydberg atom arrays

We report on the ground state phase diagram of interacting Rydberg atoms in a two dimensional square lattice array, a promising platform for quantum information processing. Using new developments in tensor network algorithms, we are able to study with high fidelity the phases in the bulk as well as their analogs in large, experimentally accessible finite arrays by including all long-range interactions. We find that much of the phase diagram consists of crystalline and quantum mean-field-like ground states, akin to proposals in the literature although significantly altered in our high-accuracy treatment. However, we also discover a hitherto hidden region of an unusual ordered quantum phase with non-trivial entanglement. Broadly, our results yield a conceptual guide for future experiments, including where to look for interesting physics.   

Lifetime of Near-Threshold Multiparticle Resonances: From Q-balls to helium-3 droplets

We consider a system of N nonrelativistic particles which form a near-threshold resonance. Assuming no subset of these particles forms a bound state, the resonance can decay only to N particles. We show that the decay width of the resonance scales as E^Δ-5/2 where ∆ is the ground state energy of a system of N particles in a spherical harmonic trap with unit frequency. The formula remains to be valid when some of the final particles have resonant s-wave interaction with each other, provided that the Efimov effect is not present. In the limit of large N, we show that the spectrum of final particles is the Maxwell-Bolzmann distribution in the case of bosons, and follows a semicircle-like law in the case of fermions. We argue that metastable ³He droplets exist with the lifetime varying over many orders of magnitudes ranging from a fraction of a nanosecond to values much larger than the age of the Universe.   

Strain-induced Superfluid-Insulator Transition for Atoms Adsorbed on Graphene

Strongly correlated bosons deposited on an atomic mono-layer substrate are an exciting playground to engineer two-dimensional (2D) quantum phases for both theoretical and experimental physics. It is known that the first layer of 4He adsorbed on graphene is a strongly correlated insulator, with subsequent layers displaying superfluid, and even possibly supersolid-like order. In this talk, we explore the possibility of a quantum phase transition between insulating and superfluid phases by applying uniform isotropic strain to graphene. As the strain increases, changes in the adsorption potential drastically alter the phase boundary of the 2D atom layer. It leads to a variety of Mott phases with different filling fractions unrealized in the triangular lattice hard-core Bose-Hubbard model. Using large-scale quantum Monte Carlo simulations, we determine the low temperature phase diagram which displays robust superfluidity in the first layer, which is analyzed within the context of Kosterlitz-Thouless theory. In the zero temperature limit, we discuss a possible quantum phase transition between insulating and superfluid states driven solely by the uniform strain.   

2D Extended Bose-Hubbard Model for Light Atoms on Graphene

An exciting development in the field of correlated systems is the possibility of superfluidity for a single layer of helium atoms adsorbed on novel two-dimensional quantum materials such as Graphene. This complex many-body problem can be mapped onto an effective extended Bose-Hubbard model on the triangular lattice extracted with high precision from a high-energy microscopic description. The helium atoms behave as hard-core bosons, and the ratios of the hopping parameter to the interaction strengths control the nature of the emergent many-body state. Using mean-field theory we show how the insulating phases at fillings 1/3, 2/3, and 1 emerge and compete with superfluidity as the graphene substrate is uniformly strained. In contrast to pristine unstrained graphene - where the 1/3 atomic solid is always favorable and 2D superfluidity is not present - applying a moderate uniform strain allows 2D superfluidity to emerge in a large region of parameter space, now competing with the higher filled (2/3 and 1) solid phases. This analysis opens the door towards designing purely 2D superfluids by manipulating the atomically thin substrate underneath.   

Ballistic magnetotransport and field-induced interaction effects in graphene.

A weak perpendicular magnetic field, B, breaks the chiral symmetry of each valley in the electron spectrum of graphene, preserving the overall chiral symmetry in the Brillouin zone. We explore the consequences of this symmetry breaking for the interaction effects in graphene. In particular, we demonstrate that: 1) the electron-electron interaction lifetime acquires an anomalous B-dependence. Also, the ballistic zero-bias anomaly emerges at a weak B that has an algebraic form. 2) The perpendicular magnetic field introduces an anomalous interaction correction to the static conductivity of doped graphene in the ballistic regime. The correction implies that the magnetoresistance scales inversely with temperature $\prop 1/T$ in a parametrically large interval. When the disorder is scalar-like, the $\prop 1/T$ behavior is the leading contribution in the crossover between diffusive regime exhibiting weak localization and quantum magneto-oscillations. 3) Temperature dependence of the magnetic-field corrections to the thermodynamic characteristics of graphene is also anomalous.   

Understanding the effect of beyond-Fröhlich interactions on large polarons

The large polaron, an electron interacting with a continuum of lattice phonons, is one of the most fundamental and well-known problems of many-body physics. Large polarons are often described using the Fröhlich Hamiltonian, which assumes a linear electron-phonon interaction. However, in recent years significant interest has been raised in additional interaction terms, such as the 1-electron-2-phonon interaction. In our work, we extend Fröhlich theory to include this interaction and investigate the properties of the resulting polaron.

We derive an analytical expression for the interaction strength of an electron coupling to LO phonons. For cubic materials, the interaction strength only depends on a single scalar parameter, making it well-suited for analytical calculations. Since the resulting Hamiltonian is quadratic, we may investigate several properties using the path integral formalism: these include the energy and effective mass of the new polaron, and formation of bipolarons. It is shown that the additional term leads to significant additional trapping of the electron, broadens the bipolaron stability regime, and causes a secondary absorption peak in the optical conductivity.   

Spin-charge separation with tunable interaction strength

We report on the observation of spin-charge separation in a Tomonaga-Luttinger liquid (TLL) with tunable interaction strength. We measure the dynamic structure factor (DSF) for both the spin and charge modes for various strengths of repulsive interaction, and compare these to calculations using Bethe ansatz results and the local density approximation. Our experiment employs fermionic ultracold ⁶Li atoms confined in an array of quasi-one-dimensional tubes produced using a two-dimensional optical lattice. The gas is a spin-balanced mixture of two hyperfine sublevels, which constitute a spin-1/2 system. Using Bragg spectroscopy we separately excite low-energy spin and charge waves in order to obtain the DSFs for each mode. Our measurements are in good agreement with our calculations, indicating an increasing charge-mode velocity and a decreasing spin-mode velocity with increasing interaction strength, as expected according to TLL theory. Furthermore, our spin-mode measurements for strong interactions show a high-frequency tail that we show is a result of the nonlinear Luttinger liquid.   

Dynamical mean-field theory analysis of the quantum Zeno effect in a driven-dissipative Bose-Hubbard lattice

The study of the driven-dissipative quantum many-body problem has gained, in the last decade, considerable traction. Photonic systems, in particular, have emerged as particularly suited platforms thanks to the ease of introduction of driving and dissipation, and the latter has been harnessed as a convenient tool for the preparation of strongly-correlated many-body states. Despite these recent efforts, the picture on driven-dissipative many-body quantum systems is still incomplete and calls, among others, for the development of new, powerful numerical methods which are able to cope with the sheer size of the Hilbert space and, at the same time, to carefully handle the presence of correlations. In this work, we overcome these problems by employing the DMFT technique in the context of driven-dissipative bosonic lattices. As a case study for the effectiveness of our specific implementation of this technique, we demonstrate the ability to reproduce the so-called quantum Zeno effect in a Bose-Hubbard lattice of cavities with strong two-particle dissipation.

References

1. Seclì et al, New J. Phys. 23, 063056.

2. Seclì et al, in preparation.   

Effective models derived for the hydrogen chain using correlated many-body wave functions

It is challenging in first-principles calculations to elucidate the mechanisms underlying phase transitions in complicated materials where multiple interactions, such as electron-electron and electron-phonon interactions, play essential roles. With the help of model Hamiltonians, one can isolate specific interaction channels and study how they compete or collaborate to generate the plethora of phases. This work proposes a general procedure to derive accurate interacting Hamiltonians in a simple system, the hydrogen chain, using correlated many-body wave functions generated using fixed-node diffusion Monte Carlo. We show that the effective on-site Coulomb repulsion $U$ and double occupancy compensate and give rise to a nearly constant on-site interaction contribution to the total energy during dimerization. Our results show that the electron hoppings contribute to the energy drop the most when the chain dimerizes. This work lays out the workflow of deriving models using the highly accurate first-principles method and demonstrates how to establish causation of certain effective interactions during phase transition.   

Optimized Basis Sets for Electron Correlation in Solids: Energies and 1RDM

Basis incompleteness is a significant source of error in orbital-space electronic structure methods. This problem is particularly acute in solids where readily available bases, e.g. mean-field orbitals and atomic basis sets, can lead to slow and non-linear convergence to the complete basis set (CBS) limit. In this work, we show that optimized Gaussian orbitals can be used to construct fast and smoothly converging correlation-consistent basis sets. CBS energies can be obtained from cc-pVTZ and cc-pVQZ extrapolation in ionic crystals. The same is true in alkaline metals once a single shell of plane waves are added. By analyzing the one-body reduced density matrix in real and reciprocal space, we show that the optimized basis set captures the correct correlation energies for the right reasons: physical charge density and momentum distribution.