Realization of a Rydberg-dressed extended Bose Hubbard model

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Hi, I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Realization of a Rydberg-dressed extended Bose Hubbard model".

Mira: Here's the gist of the paper. The gist: This work realizes an effective one-dimensional extended Bose-Hubbard model using Rydberg-dressed 87Rb atoms in an optical lattice, overcoming experimental challenges to probe correlated out-of-equilibrium dynamics and density ordering in this system.

Kai: Rydberg Dressing Mechanism Off-resonant admixture of strongly interacting Rydberg states, or “Rydberg dressing”, offers an alternative pathway to realize extended-range interacting quantum gases that are compatible with in-situ control over single atoms and provides flexible interaction control Rydberg dressed interactions emerge through the off-resonant coupling of short-range interacting ground state atoms to a higher-lying, long-range interacting Rydberg state with Rabi frequency omega and detuning ∆ The Rydberg blockade modifies the AC Stark shift experienced by two nearby ground state atoms, which leads to a characteristic softcore-shaped potential with softcore height V0 = omega4/(8∆3) and tunable interaction range Rc = (C6/(2ħ∆))1/6 of up to a few lattice sites, with an asymptotic van-der-Waals tail and coefficient C6 The optical coupling also provides a unique handle to control the interaction, for example, to realize sudden quenches of the interaction strength on submicrosecond timescales, periodically-modulated interactions

37: or turning on the long-range interactions only after the system has been prepared Experimental Realization and Control The experiment uses up to 200 87Rb atoms in a single plane of a vertical optical lattice, realizing a two-dimensional Bose-Hubbard model using a folded lattice with lattice spacing alat = 752 nm, tunable tunnel coupling J and approximately fixed interaction strength U/h = 225 Hz Single-site addressing is used to prepare three parallel and independent one-dimensional (1D) systems oriented along the x-direction and separated by at least three lattice sites in the y-direction Tunneling along the x-direction is enabled at a rate J, while tunneling along the transverse y-direction is inhibited by apply−5 0 5 Extended-range interactions up to two-lattice sites are induced by off-resonantly coupling atoms from the ground state g⟩ to the r⟩ = 30P3/2; mj = +3/2⟩ Rydberg state with an ultraviolet laser at a wavelength of 297 nm The resulting time-averaged interaction strength V is calibrated using a spectroscopic spin-echo sequence

52: Out-of-Equilibrium Dynamics The study probes the correlated out-of-equilibrium dynamics of extended-range repulsively-bound pairs at low filling, and kinetically constrained “hard rods” at half filling Near equilibrium, the researchers observe density ordering when adiabatically turning on the extended-range interactions They first observe the existence and dynamics of repulsively-bound pairs of atoms occupying neighboring lattice sites stabilized by strong extended-range interactions Increasing the filling, at large nearest-neighbor interaction, they realize a gas of “hard rods” and demonstrate the striking difference in the density relaxation of an initial chargedensity wave of such hard rods compared with the case of hard-core bosons Near-Equilibrium Density Ordering The researchers aim to study the eBHM near equilibrium by realizing a 1D lowenergy state near the many-body ground state at halffilling in absence of long-range interactions They subsequently adiabatically expand the system into a one-dimensional chain of 17 sites by lowering the external confinement potential over a timescale of ∼ 60ħ/J

52: As they linearly increase the nearest-neighbor interaction from V = 0 to V = 10.0(6)J over a timescale corresponding to ∼ 2.9 tunneling times, they observe the emergence of density-ordering into a state similar to the quantum solids that were recently observed in magnetic dipolar atoms

21: They find that with increasing interaction V, the nearest- (Cd=1) and next-nearest (Cd=2) neighbor correlation strengths decrease and increase, respectively, indicating the onset of density-ordering in their system Key Findings on Dynamics and Control The stroboscopic dressing sequence enables significantly increased lifetimes of over 100 ms in their system, surpassing previous observations by two orders of magnitude The pulsed scheme improves the product of the time-averaged interaction times lifetime, as V τ ∝ 1/∆

53: and effectively scales as √3 D−1 if the time-averaged softcore height is kept constant

52: The group velocity of the unbound atoms are kept constant for the fit and are independently derived from case ○5 of the main text For larger ramp durations, they observe a temperature mismatch between Cd=1 and Cd=2, indicating that the system did not fully re-thermalize after an atomloss event The simulation using matrix-product-state (MPS) formalism shows that the short ramping protocol with tf = 3.0 ħ/2J already results in a simulated preparation fidelity of F = 62% Future Directions The work opens perspectives for extending the study from one-dimensional systems to ladder systems

62: , towards twocomponent mixtures with only one featuring long-range interactions

63: or to leave the hard-core boson limit and explore the full V /J − U/J phase diagram of the extended Bose-Hubbard model which is expected to include the celebrated Haldane insulator

3, 64: Exploring lowenergy physics in extended-range interacting fermionic systems, may be relevant to understanding 1D cuprate chains

65: and the constrained dynamics of the hard rod model out-of-equilibrium realized in the presence of the extended interactions is an exciting frontier

59: Acknowledgments The authors gratefully acknowledge discussions with Simon Hollerith, Waseem Bakr and his entire team, Matthew Eiles, Markus Greiner, Daniel Malz and Markus Heyl They acknowledge funding by the Max Planck Society (MPG), the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy–EXC-2111–390814868 and through the DFG Research Unit FOR 5522 (project-id 499180199) as well as Project No.

Mira: BL 574/15-1 within SPP 1929 (GiRyd) This publication has also received funding under the Horizon Europe program HORIZON-CL4-2022-QUANTUM-02-SGA via the project 101113690 (PASQuanS2.1) P.W.

Kai: acknowledges funding through the Walter Benjamin program (DFG project 516136618) J.Z.

Title and authors: Kai: So we're looking at this paper now called "Realization of a Rydberg-dressed extended Bose Hubbard model". It’s not just a theory; it’s showing how to actually build something physical that behaves like this specific model.

Mira: The core idea they are focusing on is bridging the gap between the abstract, extended Bose-Hubbard model and an experimental setup where you can actually test those long-range interactions. They use Rydberg dressing as the tool to engineer those interactions in a way that you can control it.

Lev: So when we look at this, it’s about taking a system that normally has short-range hopping and on-site repulsion and adding this tunable, extended repulsive interaction that goes beyond just the nearest neighbors.

Kai: Exactly. They do this by off-resonantly coupling atoms in the ground state to a higher lying Rydberg state with a Rabi frequency Omega and a detuning Delta, which fundamentally changes how neighboring atoms experience the AC Stark shift.

Mira: The key thing they point out is that this Rydberg blockade creates a softcore potential with a height V0 equal to Omega to the power of four over eight times Delta cubed and an interaction range Rc proportional to the inverse sixth power of the detuning <ref:2405.20128#pg1>.

Lev: Having that interaction range Rc being tunable by adjusting Delta gives you flexibility, which is crucial because if you can't tune it, you can't really study that extended-range physics they are interested in.

Kai: And the authors show how this dressing mechanism also lets them do sudden quenches of the interaction strength on submicrosecond timescales, or even periodic modulation of these interactions.

Mira: That temporal control is a big deal because it allows them to study things that happen during fast evolution, which is often difficult to capture with static interactions.

Lev: But those fast control pulses put stress on the system's coherence and stability; you have to make sure the noise from the dressing laser doesn't destroy the delicate many-body physics they are trying to measure.

The paper's summary: Kai: So, summarizing what this paper actually did with this "Realization of a Rydberg-dressed extended Bose Hubbard model," they used up to two hundred eighty seven atoms in one plane of a vertical optical lattice to build this model. They set up three independent one-dimensional systems running along the x-direction and spaced by at least three lattice sites in the y-direction.

Mira: That setup allowed them to engineer tunneling along the x-direction with a rate J, while they kept tunneling along the transverse y-direction inhibited by applying a potential of five times zero point five.

Lev: So they effectively created three separate one-dimensional systems that are only weakly coupled transversely, which is a classic way to isolate and study one dimension at a time in optical lattice experiments <ref:2405.20128#pg1>.

Kai: They then induced these extended-range interactions up to two lattice sites by off-resonantly coupling atoms from the ground state g> to the Rydberg state r> with an ultraviolet laser at a wavelength of two hundred ninety-seven nanometers.

Mira: This results in a time-averaged interaction strength V that they calibrated using a spectroscopic spin-echo sequence, which gave them a specific value of V equals two hundred twenty five hertz.

Lev: Calibrating the interaction strength with spectroscopic sequences is necessary because the actual optical coupling strength can drift, so you need a reliable measurement to know what your interaction parameter actually is.

Kai: The paper then goes on to study the correlated out-of-equilibrium dynamics of extended-range repulsively bound pairs at low filling and kinetically constrained "hard rods" at half filling near equilibrium.

Mira: These are specific regimes where they are looking for density ordering, and they found that when they adiabatically turn on these extended interactions, they first observe the existence and dynamics of repulsively bound pairs stabilized by those strong extended-range interactions.

The paper's improvements: Kai: One major finding is that increasing the filling further, at large nearest-neighbor interaction strength, they realize a gas of "hard rods" and they demonstrated the striking difference in the density relaxation of an initial charge density wave of such hard rods compared to the case of hard-core bosons.

Mira: That comparison between hard rods and hard-core bosons is telling because it highlights how different the dynamics are when you have these extended interactions versus just standard short-range interactions.

Lev: For someone building hardware, tracking that difference in density relaxation is important because it tells you what kind of physics you’re actually seeing, not just some generic many-body behavior.

Kai: They also focused on studying the near-equilibrium Bose-Hubbard model by preparing a one dimensional low energy state near the many-body ground state at half filling in absence of long range interactions <ref:2405.20128#pg1>.

Mira: They then adiabatically expand that system into a one dimensional chain of seventeen sites by lowering the external confinement potential over a timescale of about sixty times h divided by J.

Lev: That ramp time is important because it sets the scale for how fast you can change your parameters without driving the system into unwanted excitations, and sixty times h divided by J is a critical time scale in these types of experiments.

Kai: As they linearly increase the nearest-neighbor interaction from V equals zero to V equals one point zero six times J over a timescale corresponding to about two point nine tunneling times, they observe density ordering into a state similar to the quantum solids that were recently observed in magnetic dipolar atoms.

Mira: That observation of density ordering as you ramp up the interaction strength, where nearest-neighbor correlations decrease and next-nearest neighbor correlations increase, is a very specific signature for what they are describing.

Conclusion: Kai: So to wrap up this paper "Realization of a Rydberg-dressed extended Bose Hubbard model," it shows that you can physically build a simulator for an extended Bose Hubbard model using Rydberg dressing.

Mira: The main implication is that we now have a method to study the correlated out-of-equilibrium dynamics and density ordering in these systems using this specific physical realization.

Lev: For us building hardware, it means the next step is taking these protocols and figuring out how to map them onto actual qubit architectures, which involves tackling the overhead of implementing those fast dressing pulses and achieving that high fidelity preparation.

Kai: It opens up avenues for studying ladder systems, twocomponent mixtures with only one featuring long-range interactions, or even exploring the full V over J minus U over J phase diagram of the extended Bose-Hubbard model which includes things like the Haldane insulator.

Mira: They also point towards exploring low-energy physics in extended-range interacting fermionic systems, which could be relevant to understanding things like one dimensional cuprate chains or the constrained dynamics of hard rod models out-of-equilibrium.

Lev: The paper's limitation is that they focus heavily on one dimension and they don't fully explore the full phase diagram, so extending these results to three dimensions would be a huge challenge.

Kai: That’s fair; extending this into three dimensions is definitely the next big experimental hurdle for people trying to get these kinds of results from actual atoms.

Mira: But overall, it’s a solid demonstration of realizing a controllable extended-range interaction using Rydberg dressing that opens up new ways to look at correlated dynamics in these systems.

Lev: The realization of this Rydberg-dressed extended Bose Hubbard model is an important step forward for testing the limits of what we can do with these quantum simulators today.