Session N08: Long-Range or Anisotropic Interactions

Ultrafast Quantum Many-body Dynamics of Rydberg Excited Atomic Mott-Insulator Lattice

An ensemble of Rydberg atoms is a unique platform for quantum simulation and quantum computation. In our research group, we are developing a novel approach for Rydberg-based quantum simulations and computations, where we use broadband pulsed lasers to excite ⁸⁷Rb atoms, in Bose-Einstein condensates (BECs), Mott-Insulator (MI) lattice and optical tweezers, to Rydberg states in a timescale of 10 to 100 picoseconds at the speed limit set by the Rydberg splitting [1-4].

           In my presentation, I will give the overview of our ultrafast quantum simulator in which we generate a strongly correlated ultracold Rydberg ensemble of ⁸⁷Rb atoms excited from an unity filling MI [1,3,4]. We observe and control its ultrafast many-body electron dynamics by performing the time-domain Ramsey interferometry with attosecond precision [3].  I will also discuss our recent observation of the strong spin-motion coupling emerging from the large variation of the interaction potential over the wavefunction spread by exciting the atoms to the Rydberg S state from the unity filling MI[4].  In the present experimental condition, the momentum kick was found non negligible because of the short Rydberg-Rydberg distance. Finally, in the outlook, I will discuss about the exciting proposal to bring the timescales of Rydberg interaction and motion of the atom together to investigate a larger class of Hamiltonians with ultrafast stroboscopic Rydberg excitation. In this novel approach the strength of the spin-motion coupling can be tuned arbitrarily relative to the motional energy scale set by trapping potentials [4].

    

Physics of Rydberg atoms in inhomogeneous electric fields

Charge-neutral interactions are of fundamental interest in physics and chemistry, and recent experiments are beginning to explore them within the quantum regime. Rydberg excitations offer a route toward tunable atom-ion interaction strengths and the sensitivity of Rydberg atoms to electric fields enables them to form long-range weakly-bound diatomic molecular ions. These dimers bind on micrometer length scales due to the Rydberg's large induced dipole moment, which is the leading-order term in the ion-neutral interaction series. Our work explores the role of the higher-order multipole terms in this interaction series, focusing on emergent physics as a result of the ion's inhomogeneous electric field. Surprisingly, we find that the Rydberg atom's quadrupole may compensate the enormous Coulomb repulsion between a pair of cations, forming a metastable doubly-charged trimer. Additionally, the quadrupole interaction term introduces an unexpected dependence on the sign of the ion's charge, which can significantly alter non-adiabatic couplings between potential energy curves. These modified couplings would not only affect vibrational dynamics, but also lifetimes of bound dimers.   

Rydberg molecule formation by a Rydberg atom in atomic Fermi superfluid

We consider a Rydberg atom immersed in a two-component atomic Fermi superfluid. The electron-atom scattering results in an attractive potential for the atoms in the superfluid to form a Rydberg molecule. The Fermi superfluid is formulated by the BCS-Leggett theory, and we solve the Bogoliubov-de Gennes (BdG) equation of the ground state with the Rydberg potential from first-principle calculations of selected Rydberg states. Analyzing the bound states from the BdG equation then identifies the formation of Rydberg molecules. On the BCS side with weak pairing interaction, the Rydberg potential typically breaks a Cooper pair and forms a Rydberg molecule between the Rydberg atom and a broken-pair fermion. On the BEC side, however, depending on the depth of the Rydberg potential, a Rydberg molecule between a Rydberg atom and a Cooper pair, or "pair in molecule", can emerge as a tightly bound Cooper pair falls into the Rydberg potential. The wavefunctions and energy spectrum from the BdG equation further demonstrate the rich physics behind Rydberg molecules in atomic Fermi superfluid.   

Magnon decays in dipolar Rydberg quantum simiulators

Spin-waves or magnons are the elementary quanta of excitation on top of ordered magnetic phases, such as ferromagnets and antiferromagnets. Although generally stable in short-range interacting systems, a magnon can spontaneously decay into two in presence of a magnetic field. Motivated by the recent experimental realization of magnetism in long-range interacting Rydberg arrays, we will consider the problem of stability of magnons in presence of an external field. We will discuss symmetry and kinematic constraints on such decays, and the essential differences between short-range and long-range interacting models. If time permits, we will comment on the physical consequences of magnon decay as they pertain to correlation functions and spin transport.    

Interspecies Förster resonances of Rb-Cs Rydberg d-states for enhanced multi-qubit gate fidelities

Neutral atoms arrays have become a prominent platform for quantum computation due to the scalability of optical tweezers allowing for up to 1000 identical qubits, in which multi-qubit gates are mediated by interactions between highly excited Rydberg states. To realise fault tolerance on a neutral atom platform it is necessary to be able to perform independent and cross-talk free mid-circuit readout of ancilla qubits. One approach to overcome this limitation is to use dual-species arrays, which naturally provides a separation in read- out wavelengths to suppress cross-talk, whilst allowing engineering of different inter and intra-species couplings.

We present an analysis of interspecies interactions between Rydberg d-states of rubidium and cesium. We identify the Förster resonance channels offering the strongest interspecies couplings, demonstrating the viability for performing high-fidelity two- and multi-qubit CkZ gates up to k=4, including accounting for blockade errors evaluated via numerical diagonalization of the pair-potentials. Our results show d-state orbitals offer enhanced suppression of intraspecies couplings compared to s-states, making them well suited for use in large-scale neutral atom quantum processors.   

Two-mode squeezing in Floquet engineered power-law interacting spin models

We study the non-equilibrium dynamics of a quantum spin 1/2 XXZ model realized in a two-dimensional bi-layer system, with couplings mediated by inverse power-law interactions, falling off with distance r as 1/r^α. Starting from an initial state of spins with opposite magnetization in the two layers we find exponential growth of correlated pairs of excitations. We demonstrate that for a broad range of parameters, the system shows collective behavior resulting in exponential generation of entanglement. Specifically, we study the effects of the range of the interactions via the inverse power, α, and the interlayer spacing, a_Z, on the entanglement dynamics. This work demonstrates that metrologically useful entanglement in the form of two-mode squeezed states separated in bilayers can be generated via power-law interactions, making it accessible in a wide variety of experimental atomic, molecular, and optical platforms, with potential applications in quantum-enhanced sensing.   

Phase space and tensor network methods for two-dimensional quantum dynamics with power-law interactions

A key goal in modern quantum science is to harness the complex behavior of quantum systems to develop new technologies. While precisely engineered platforms with ultracold atoms and trapped ions have emerged as powerful tools for this task, our limited ability to theoretically and numerically model these systems poses immense challenges for their improved control and characterization. Here, I discuss the application of modern computational techniques, including tensor networks and efficient phase space methods, to study the quantum dynamics of many-body systems, with features relevant for an array of current experiments. As a specific case study, I will present strategies for the robust generation of spin squeezed states – a special type of entangled resource that can be used for enhanced precision sensing – in current quantum sensors. Beyond applications for current experiments, including arrays of Rydberg atoms, polar molecules, and trapped ions, these studies shed light on the fundamental behavior of canonical models for quantum chaos and quantum magnetism.   

How solid is a dipolar supersolid?

The conceptual roots of supersolidity can be traced back to 1960, when Eugene Gross calculated the appearance of long-range spatial order in the ground state of a system of interacting bosons. In 2004, an abrupt change in the shear modulus of solid Helium-4 was interpreted as the first experimental evidence of a solid-to-supersolid transition. However, this proved to be a false dawn, with the shear modulus shift arising from structural changes in the classical solid instead. The eventual experimental observation materialized via a superfluid-to-supersolid phase transition in ultracold gases, with particular success in dipolar Bose Einstein condensates (BECs) [1]. To complement this robust experimental platform, we use the extended Gross-Pitaevskii equation (eGPE) to theoretically probe the distinctly solid properties of the supersolid. We shear the crystal to produce perpendicular shear waves in the supersolid --- this transverse wave only propagates in solids, and can be probed across the BEC-to-supersolid transition. We find the appearance of a non-zero shear modulus at the BEC-to-supersolid transition, which increases as the superfluid fraction is reduced. Our results match closely with a semi-analytic model for the crystal deformation.

[1] L. Chomaz et al., Rep. Prog. Phys. 86 026401 (2022).   

Dipole-dipole interactions inside electron-hole plasma

We numerically investigate the effects of electron-hole plasma on excitonic states as well as its effects on dipole-dipole interactions between coupled exitons. In our model, we treat the dipole as a fixed central positive charge and a harmonically trapped negative charge oscillating around it in an eigenstate of a harmonic oscillator or a superposition of multiple eigenstates. We numerically evolve the electron and hole constituents of the plasma through classical electric interactions with each other and with the dipole charges. However, we follow the state of the oscillating dipole by tracking the change of its quantum Wigner function and its projection on the different eigenstates of the harmonic oscillator eigenstates. Our analysis shows that, through the interaction with the plasma particles, the quantum Wigner distribution of the dipole turns into a classical phase space distribution without any negative regions on the phase space. We also investigate the dipole-dipole interactions between two such dipoles and the effect of the plasma on the transfer of energy between them.   

From conditional phase to quantum vortices of photons

Vortices are a hallmark of topologically nontrivial dynamics in nonlinear physics. They appear in optics as phase twists in the electromagnetic field resulting from light-matter interactions. Quantum vortices, characterized by phase singularities in the wavefunction, are typically associated with strongly interacting many-particle systems, particularly superfluids. However, the emergence of vortices through the effective interaction of light with itself, a phenomenon requiring strong optical nonlinearity, was previously limited to the classical regime until recent advancements.

We report on the realization of quantum vortices of photons that result from a strong photon-photon interaction in a quantum nonlinear optical medium. The interaction causes faster phase accumulation for co-propagating photons, producing a quantum vortex-antivortex pair within the two-photon wave function.

For counter-propagating photons, a conditional phase and a non-trivial intensity correlation between the photons are also observed. Furthermore, if the photons have different parity, they exchange their parity by the long-range dipole-dipole exchange interaction by imprinting a pi/2 conditional phase. 

For three photons, the strong interaction leads to an even richer topological structure of the three-photon wavefunction. The point vortices lead to the formation of vortex lines, and a central vortex ring attests to a genuine three-photon interaction. It also produces chiral asymmetric interactions between the photons.  

The wavefunction topology, governed by two- and three-photon bound states, imposes a conditional phase shift of pi-per-photon, a potential resource for deterministic quantum logic operations.