Negative Interaction Quench Dynamics of Density-Ordered Dipolar Bosons in a One-Dimensional Optical Lattice

Using the numerically exact multiconfigurational time-dependent Hartree method, this study reveals that a negative interaction quench in a one-dimensional dipolar Bose gas induces rich tunneling dynamics across superfluid, Mott-insulating, and fragmented regimes while remarkably preserving underlying crystal-state correlations, thereby establishing such systems as a versatile platform for nonequilibrium quantum simulation.

The Gist

Imagine a tiny, one-dimensional stage made of three deep pits (an optical lattice). On this stage, we place six very special dancers: dipolar bosons. These aren't ordinary dancers; they are like magnets that repel each other strongly when they get too close, but they also have a long-range "grudge" that keeps them apart even across the whole stage.

In the beginning, these six dancers are in a Crystal State. Because they hate being near each other so much, they have arranged themselves in a perfect, rigid line: one dancer in the center of each pit, and one dancer in the middle of the space between the pits. They are frozen in a highly organized, "crystalline" formation.

The Experiment: The "Snap"

The researchers decided to test how stable this perfect formation is by performing a "negative interaction quench." Think of this as suddenly turning off the dancers' "repulsion magnets."

They took the system from a state where the dancers were fiercely repelling each other (strong long-range interactions) and suddenly switched it to a state where they barely repel each other at all (short-range interactions). They did this three different ways, aiming for three different final "moods" for the dancers:

1. The Superfluid Mood: The magnets are turned off completely. The dancers should become a free-flowing, chaotic fluid.
2. The Mott-Insulator Mood: The magnets are turned down just a little. The dancers should settle into a rigid, block-like pattern.
3. The Fermionized Mood: The magnets are turned down to a medium level. The dancers should act like they are avoiding each other so much they can't even share a spot, but not quite as rigid as the crystal.

What Happened? The Big Surprise

Usually, if you suddenly remove the rules that keep a group organized, you expect total chaos. You'd expect the "crystal" to melt instantly, the dancers to run everywhere, and the perfect order to vanish.

But that's not what happened.

The paper found that the crystal's "memory" is incredibly strong. Even after the "repulsion magnets" were turned off or weakened, the dancers didn't immediately scramble into a chaotic mess. The underlying order of the crystal state remained surprisingly robust.

Here is how the dancers behaved in each scenario, using simple analogies:

• In the "Superfluid" Scenario (Total Repulsion Off):
  You might expect the dancers to rush out of their pits and mix everywhere. Instead, they mostly stayed put. They didn't run across the stage to swap places with neighbors. Instead, they started doing a local "sloshing" dance. Imagine a cup of water; if you nudge it, the water wiggles back and forth inside the cup, but it doesn't spill over to the next cup. The dancers wiggled and breathed inside their own specific spots, but they didn't break the crystal's global order. The "crystal" didn't melt; it just started vibrating.

• In the "Mott-Insulator" Scenario (Slight Repulsion):
  Here, the dancers moved a little bit at first, like a brief shuffle, but then they quickly settled back down. After a short burst of activity (about 10 "time units"), they froze again. It was as if they realized, "Oh, we're still in a line," and stopped moving. The system stabilized into a new, quiet state very quickly.

• In the "Fermionized" Scenario (Medium Repulsion):
  This was the most interesting. The dancers didn't freeze, nor did they run wild. They entered a state of constant, complex motion. They kept shuffling and exchanging places, but they did it in a way that kept the overall "fragmented" nature of the system. It was like a busy dance floor where everyone is moving, but no one is leaving the room. The system remained "fragmented" (spread out across many different quantum states) rather than condensing into a single, unified flow.

The "Middleman" Pit

A key discovery was about the central pit (the middle well).

• The dancers in the left and right pits mostly stayed in their own lanes.
• The dancer in the middle pit acted as the traffic controller. Almost all the movement and "tunneling" (jumping between pits) happened through this middle spot. It was the only place where the dancers really swapped places with their neighbors. The outer pits were like quiet suburbs, while the middle pit was the busy city center.

The Takeaway

The main point of this paper is that strong correlations are tough to break.

Even when the researchers suddenly changed the rules of the game (turning off the long-range repulsion), the dancers didn't forget their formation immediately. The "crystal" structure was so deeply ingrained that it survived the shock. The system didn't just melt into chaos; it found a way to wiggle and vibrate locally while keeping its global shape intact.

The researchers also showed that by adjusting the depth of the pits (the stage) at the same time they changed the repulsion, they could control exactly how much the dancers moved. This proves that these systems are excellent "simulators" for studying how complex quantum systems react to sudden changes, showing that order can persist even in the face of chaos.

In short: You can pull the rug out from under a perfectly arranged crystal of quantum particles, and instead of falling apart, the crystal just starts doing a very specific, localized dance while holding its shape together.

Technical Summary

Technical Summary: Negative Interaction Quench Dynamics of Density-Ordered Dipolar Bosons in a One-Dimensional Optical Lattice

Problem and Motivation
Ultracold atomic gases in optical lattices serve as controllable platforms for studying nonequilibrium dynamics in strongly correlated quantum systems. While tunneling dynamics in short-range interacting systems are well-established, the role of long-range interactions in quantum quenches remains largely unexplored, particularly in finite-size systems where correlations are strongest. Dipolar ultracold atoms exhibit long-range, anisotropic interactions that stabilize unconventional quantum phases, such as density-wave phases and crystalline states, distinct from standard contact-interacting Bose-Einstein condensates. A key motivation for this work is to understand the robustness of these crystal-state correlations under dynamical perturbations, specifically when the system is driven from a long-range interaction-dominated regime to a short-range interaction regime.

Methodology
The study investigates six dipolar bosons confined in a finite one-dimensional optical lattice with three sites (a triple-well lattice) and a filling factor of two. The system is modeled using a many-body Hamiltonian comprising kinetic energy, a sinusoidal lattice potential, and a dipolar interaction potential that includes both short-range contact terms and a long-range $1/r^3$ tail.

The pre-quench state is prepared as a highly correlated crystal state ($g_d = 15$) in a deep lattice ($V_0 = 8 E_r$). The dynamics are initiated by a "negative interaction quench," where the dipolar interaction strength is suddenly reduced to target regimes:

1. Superfluid (SF) regime ($g_d = 0$).
2. Mott-insulator (MI) regime ($g_d = 0.1$).
3. Fermionized Mott (FMI) regime ($g_d = 1$).
   Additionally, a combined protocol involving a simultaneous ramp-down of the lattice depth ($V_0$ from 8 to 4) is explored to probe the interplay between interaction strength and confinement.

The time-dependent many-body Schrödinger equation is solved using the Multiconfigurational Time-Dependent Hartree method for bosons (MCTDHB), implemented via the MCTDH-X package. This numerically exact approach utilizes a time-dependent basis of $M$ single-particle orbitals (with $M=24$ used in calculations) to capture fragmentation, tunneling, and collective excitations beyond mean-field approximations.

Key Observables
The dynamics are characterized through several observables:

• Dynamical Fragmentation: The time evolution of natural orbital occupations ($n_i/N$) to track the redistribution of particles among orbitals.
• Site-Resolved Position Variance ($\sigma^2_x$): Quantifies interwell tunneling and particle number fluctuations within specific lattice sites.
• Density Fluctuations: Real-space ($\delta\rho(x,t)$) and momentum-space ($\delta n(k,t)$) fluctuations to identify local excitations (breathing, dipole-like modes) and coherence changes.
• Glauber Correlation Functions: One-body ($g^{(1)}$) and two-body ($g^{(2)}$) correlations to analyze the evolution of single-particle coherence and particle-particle correlations.

Results
The study reveals that the underlying crystal-state correlations exhibit remarkable robustness against negative interaction quenches, persisting even as the system is driven toward SF, MI, and FMI regimes.

1. Robustness of Crystal Correlations: Despite the sudden reduction in interaction strength, the system does not immediately melt into a coherent condensate. Instead, the initial fragmentation remains largely preserved. The long-range ordering characteristic of the crystal state persists, with interwell tunneling remaining strongly suppressed compared to intrawell dynamics.
2. Regime-Dependent Dynamics:
   • Quench to SF ($g_d=0$): The system exhibits a "frozen" fragmentation where orbital populations do not significantly redistribute. Dynamics are dominated by weak intrawell excitations (local breathing and dipole-like oscillations) with minimal interwell particle transfer. The central well acts as the primary transport channel.
   • Quench to MI ($g_d=0.1$): A transient phase of particle motion occurs, followed by rapid stabilization. Orbital populations redistribute slightly before freezing, and density fluctuations settle into a quasi-stationary, localized state with suppressed tunneling after $t \approx 10$.
   • Quench to FMI ($g_d=1$): This intermediate regime displays the richest dynamics. The system remains dynamically active over longer timescales, with continuous fluctuations in orbital occupations and persistent interwell tunneling. The system explores a larger portion of the Hilbert space without condensing, maintaining a fragmented, strongly correlated character.
3. Correlation Dynamics: Analysis of $g^{(1)}$ and $g^{(2)}$ confirms that while off-diagonal coherence emerges transiently during the quench, the system stabilizes into a state where short-range correlations dominate, yet the memory of the initial long-range order (via persistent fragmentation) remains.
4. Combined Quench (Interaction + Lattice Depth): A simultaneous reduction of interaction strength and lattice depth reveals distinct dynamical regimes. The central well remains a continuous transport channel, while edge wells transition from complex, multi-frequency tunneling at weak interactions to regular, single-frequency oscillations at stronger interactions.

Significance and Claims
The paper claims that the primary significance of these findings lies in the demonstrated resilience of long-range ordered crystal states against nonequilibrium perturbations. The authors assert that:

• Robustness: Strong initial correlations in dipolar systems can survive sudden interaction changes, preserving the fragmented nature of the state even when driven toward regimes typically associated with delocalization or standard Mott insulation.
• Decoupling of Scales: The dynamics are characterized by a coexistence of strong intrawell excitations and weak interwell transport, suggesting that local excitations can be induced without significantly disrupting global correlation properties.
• Platform Potential: These results establish dipolar lattice systems as a promising platform for nonequilibrium quantum simulation. The ability to dynamically manipulate the interaction landscape while maintaining the integrity of crystal order offers a route for engineering correlation-driven phenomena and studying transport and relaxation in long-range interacting quantum systems.

The authors conclude that while the crystal state's long-range order is robust, the specific nature of the transient dynamics (frozen vs. active vs. stabilized) is highly sensitive to the final interaction strength and lattice depth, providing a controllable framework for exploring few-body quantum dynamics.