Kinematic reversibility in a low Reynolds number cold atom fluid

This study demonstrates that a magneto-optical trap acting as a low Reynolds number cold atom fluid exhibits kinematic reversibility under controlled external forces despite interparticle interactions, while also revealing conditions where system hysteresis leads to deviations from this reversibility.

The Gist

Imagine you are stirring a pot of thick honey with a spoon. If you push the spoon forward, the honey swirls and moves. If you immediately pull the spoon backward with the exact same force, the honey doesn't just flow backward; it actually retraces its steps perfectly, returning to the exact shape it had before you started. In the world of very thick, slow-moving fluids (where "inertia" or the tendency to keep moving doesn't matter), this is called Kinematic Reversibility.

This paper takes that concept and tests it using a cloud of super-cold atoms instead of honey. Here is the story of what they found, explained simply:

The Setup: A Cloud of "Atomic Honey"

Usually, when scientists study cold atoms, they look at them as a frictionless gas (like a ghost moving through a room). But in this experiment, the researchers used a special setup called a Magneto-Optical Trap (MOT).

Think of the MOT as a cage made of laser beams and magnetic fields. Inside this cage, the atoms are constantly being hit by laser light. This creates a lot of "friction" or drag, making the cloud of atoms behave less like a gas and more like a thick, sticky fluid. Because the atoms are so sluggish, they are in a "low Reynolds number" state—essentially, they are moving through a world where viscosity (stickiness) rules and momentum doesn't.

The Experiment: The Magnetic Tug-of-War

The researchers wanted to see if these atoms would obey the rules of reversibility.

1. The Push: They applied a magnetic force to drag the entire cloud of atoms in one direction. The cloud stretched and squished as it moved, rearranging its internal structure.
2. The Pull: Then, they reversed the magnetic force, pulling the cloud back to its starting spot.

The Result (The Good News):
When the lasers were perfectly aligned and the system was stable, the atoms were incredibly obedient. Just like the honey, when the force was reversed, the cloud didn't just move back; it unwound itself. Every atom returned to its exact original position, and the cloud regained its exact original shape. It was as if time had been rewound. This proved that even though the atoms were interacting with each other (bumping and pushing), the "sticky" nature of the system allowed for perfect reversibility.

The Twist: When Things Get "Stuck"

However, the paper also discovered that this perfect reversibility isn't a magic law that always works. It depends on how the "cage" is built.

In a second part of the experiment, the researchers slightly misaligned the laser beams. This created an uneven trap where the cloud of atoms split into two distinct blobs (like two grapes stuck together).

• When they pushed the cloud, atoms flowed from the top blob to the bottom.
• When they pulled it back, the atoms tried to flow back up, but they got stuck.

This is called hysteresis (or "memory"). The system remembered the path it took and refused to retrace it perfectly. The cloud didn't return to its original shape; it stayed distorted. The researchers suggest this happened because the atoms became so crowded that they "jammed" together, like a traffic jam on a highway. Once the traffic is jammed, you can't just reverse the cars to clear the road; the flow is blocked.

The Big Picture

The main takeaway is simple:

• In a smooth, well-balanced system: Cold atoms act like a perfect fluid that can be reversed exactly, just like the "3-link swimmer" described by physicist E.M. Purcell.
• In a messy, crowded, or misaligned system: The atoms can get jammed, and the system loses its ability to reverse itself.

The paper concludes that cold atoms are a fantastic "playground" for scientists to study these slow, sticky fluid dynamics. By tweaking the lasers, they can switch the system between a state where everything reverses perfectly and a state where things get stuck and irreversible, giving them a new way to study how complex fluids behave.

Technical Summary

Technical Summary: Kinematic Reversibility in a Low Reynolds Number Cold Atom Fluid

Problem and Context
Kinematic reversibility (KR) is a fundamental concept in low Reynolds number hydrodynamics, where inertia is negligible, and the trajectory of a rigid object can be exactly reversed by inverting the external force. This principle is critical in understanding biological motility and soft matter systems, where overcoming KR is necessary for unidirectional motion. While KR is well-established for non-interacting particles, its behavior in complex, interacting many-body systems remains a subject of study. Traditional cold atom systems, such as Bose and Fermi gases near zero temperature, typically operate in dissipationless regimes where viscosity is absent, rendering them unsuitable for studying overdamped dynamics. This work addresses the gap in observing KR within a cold atom system where radiative forces provide the necessary viscous damping, effectively creating a "fluid" of atomic particles subject to overdamped conditions.

Methodology
The authors utilized a magneto-optical trap (MOT) containing sodium atoms as a model low Reynolds number fluid. The system was characterized by strong damping from optical molasses, allowing the atomic cloud to behave analogously to a viscous fluid.

• Experimental Protocol: A 6-beam MOT was created with a specific laser detuning (-14.8 MHz) and magnetic field gradient (7.7 G/cm). To induce motion, a linearly ramped magnetic bias field was applied via a bias coil, effectively dragging the center of the trap. The zero of the magnetic field, $z_0(t)$, was varied linearly over a time $T$ and then reversed over a subsequent time $T$ (total duration $2T$).
• Force Dynamics: The atoms experienced a balance between the inward trapping force ($F_e = -k(z-z_0)$) and the outward radiative rescattering force. The external force followed a triangular ramp profile.
• Data Acquisition: Fluorescence images of the MOT were captured from the side at 240 frames per second. The experiment was repeated with varying ramp times ($T$) ranging from 25 ms to 10 seconds.
• Analysis: Reversibility was quantified using the Mean-Squared Deviation (MSD) of fluorescence intensity between frames. Two methods were employed:
  1. $(0, t)$ method: Compares the initial state ($t=0$) to all subsequent states to measure total distortion.
  2. $(t, 2T-t)$ method: Compares symmetric time points around the midpoint ($T$) to measure the similarity between the forward and reverse trajectories.
• Control: Background fluctuations were eliminated by subtracting the output of a control experiment.

Key Results

1. Observation of Reversibility: In well-aligned, stable MOTs, the system exhibited precise kinematic reversibility. When the external force was reversed, the atomic cloud underwent a complex three-dimensional rearrangement that was exactly undone, returning the system to its initial configuration.
2. Scaling Behavior: The degree of reversibility was found to be dependent on the ramp time $T$. The MSD between the initial and final states decreased as $T$ increased. The data followed a trend proportional to $T^{-2}$, consistent with a microscopic model where the deviation from perfect reversibility arises from the finite time response of the cloud.
3. Hysteresis and Irreversibility: The study demonstrated that KR is not a universal property of the system. Under specific MOT alignment conditions (slight misalignment), the cloud split into two distinct globes. In this "hysteretic MOT" configuration:
   • The system exhibited significant hysteresis, with the reverse motion taking considerably longer than the forward motion.
   • Atoms were transferred between the upper and lower globes, but the distribution did not return to its initial state within the experimental timeframe.
   • The MSD values were significantly higher (e.g., max MSD $\approx$ 76.8 compared to $\approx$ 21 in reversible cases), indicating a breakdown of reversibility.
   • This behavior was attributed to "jamming" caused by high atomic density and reduced mobility, where the incompressible nature of the fluid (due to rescattering forces) opposed attempts to increase density further during the reversal.

Significance and Claims
The paper claims to present the first observation of kinematic reversibility in a cold atom system. By utilizing radiative forces to create viscous damping, the authors established a versatile platform for exploring overdamped dynamics in a controllable quantum environment.

The primary significance lies in demonstrating that while strongly dissipative cold atom fluids can exhibit perfect kinematic reversibility consistent with Purcell's framework, this property is conditional. The work highlights that interparticle interactions and system geometry (specifically force balance and MOT alignment) can lead to a breakdown of reversibility and the emergence of hysteresis. The authors conclude that this system serves as a rich platform for studying the transition between reversible and irreversible behaviors, including potential phase transitions and jamming phenomena, without invoking the complex interactions found in traditional soft matter or the dissipationless nature of standard quantum fluids.