Observing dissipationless flow of an impurity in a strongly repulsive quantum fluid

Using ultracold atoms, this study demonstrates that a microscopic impurity can propagate through a strongly repulsive one-dimensional Bose gas without friction, challenging Landau's conventional expectation that superfluidity is impossible in 1D systems.

The Gist

Imagine you are walking through a crowded party. In the real world, as you try to move through the crowd, you bump into people, they bump into you, and eventually, you slow down and stop. This is friction. It's the rule of classical physics: if you push something through a fluid (like water or air), it will eventually lose its energy and come to a halt.

Now, imagine a magical party where the guests are so perfectly coordinated that if you walk through them, they don't bump into you at all. You glide through without losing a single step. This is called superfluidity, and it usually only happens at temperatures near absolute zero.

For decades, physicists believed there was a strict rule (proposed by a man named Landau) that said: "If you are a tiny particle moving through a one-dimensional line of atoms, you must eventually stop." The logic was that in a single-file line, the "crowd" is so sensitive that any movement creates ripples that drain your energy instantly.

But this new paper says: "Not so fast!"

Here is the story of what the scientists discovered, explained simply:

The Setup: A One-Dimensional Train

The researchers created a tiny, ultra-cold "train" of atoms (Cesium) inside a vacuum chamber. They squeezed these atoms into a single, narrow tube so they could only move forward or backward, like cars in a single-lane tunnel. This is their "strongly repulsive quantum fluid."

Then, they introduced a single "impurity"—a special atom acting as our runner.

The Experiment: The Sprint

They gave this runner-atom a push, sending it zooming through the tube at different speeds:

1. Slow speed: Like a gentle jog.
2. Fast speed: Like a sprint, faster than the "sound" of the crowd (supersonic).

According to the old rules, even if the runner started fast, the crowd should have created a "traffic jam" (shock waves) and slowed the runner down until they stopped completely.

The Surprise: The Ghost Runner

Here is the magic part. The runner never stopped.

• The Shock Wave: When the runner went very fast (supersonic), they did create a "shock wave"—a sudden ripple in the crowd, like a sonic boom. The crowd reacted instantly (in a tiny fraction of a second called a "Fermi time").
• The Transformation: Instead of stopping, the runner and the crowd did something weird. They "danced" together. The runner picked up a "coat" of atoms from the crowd, becoming a new, heavier, but highly coordinated entity called a Polaron.
• The Result: This new "Polaron" entity kept moving through the tube forever, maintaining a steady speed. It didn't stop. It didn't lose all its energy. It found a way to glide through the crowd without friction.

Why is this a Big Deal?

Think of it like this:

• Old View: If you try to run through a crowd of people holding hands in a line, you will get tangled, slow down, and stop.
• New Discovery: If the crowd is made of "quantum" people, you can run so fast that they don't just let you pass; they actually grab onto you and become part of your running style. You turn into a "super-runner" that the crowd supports, allowing you to keep going without ever getting tired.

The Analogy of the "Dressed" Runner

Imagine a runner trying to sprint through a field of tall grass.

• Normal Physics: The grass bends, snaps, and slows the runner down until they stop.
• This Experiment: The runner is so fast and the grass is so "quantum" that the grass doesn't just bend; it wraps around the runner's legs, forming a perfect aerodynamic suit. The runner and the grass move as one unit. The friction disappears because the grass is no longer fighting the runner; it's helping them move.

The Takeaway

This experiment proves that in the strange world of quantum mechanics, tiny objects can move through fluids without friction, even in situations where classical physics says they shouldn't be able to.

It's like discovering that if you run fast enough through a crowd, the crowd doesn't stop you—they actually help you run forever. This opens up new possibilities for understanding how information and matter move in the quantum world, potentially leading to super-fast, frictionless computers and communication systems in the future.

Technical Summary

1. Problem Statement and Context

• Classical vs. Quantum Friction: In classical mechanics, an impurity moving through a fluid inevitably experiences friction due to collisions, eventually coming to rest. In quantum fluids, superfluidity allows for dissipationless flow, but this is traditionally governed by Landau's criterion.
• The Landau Criterion Paradox in 1D: Landau's criterion states that superfluidity exists if the impurity velocity $v$ is below a critical velocity $v_c$, defined by the minimum slope of the excitation spectrum ($v_c = \min[\epsilon(p)/p]$).
  • In one-dimensional (1D) bosonic systems, the excitation spectrum (plasmon branch) dips to zero energy at finite momentum ($k = 2k_F$). Consequently, the Landau criterion predicts a critical velocity of $v_c = 0$.
  • Conventional Expectation: Based on this, any macroscopic object moving through a 1D Bose gas should experience friction and stop immediately.
• The Open Question: Does this criterion hold for a microscopic quantum impurity (a single atom) rather than a macroscopic obstacle? Theoretical work suggested that quantum effects (specifically the formation of a polaron state) might allow a microscopic impurity to move without dissipation, even in 1D, contradicting the macroscopic Landau prediction.

2. Methodology

The authors utilized ultracold Cesium-133 ($^{133}\text{Cs}$) atoms to experimentally realize and probe this scenario.

• System Preparation:
  • A Bose-Einstein Condensate (BEC) was loaded into an array of approximately 5,800 independent 1D tubes formed by a 2D optical lattice.
  • The system was tuned to the strongly interacting regime (Tonks-Girardeau gas, $\gamma \gg 1$) where bosons behave like fermions.
• Impurity Creation and Injection:
  • Creation: Impurities were created in situ within the host gas using a radio-frequency (RF) pulse to transfer a small fraction of atoms from the $(3,3)$ hyperfine state (host) to the $(3,2)$ state (impurity).
  • Acceleration: Initially, the impurity-host interaction was turned off ($\gamma_i = 0$). The impurities were accelerated by gravity to specific initial momenta ($Q$) ranging from subsonic to supersonic relative to the host gas.
  • Quench: Once the desired momentum was reached, the system was released into free fall, and the interaction strength $\gamma_i$ was rapidly ramped up (quenched) to the strongly repulsive regime.
• Dynamics and Measurement:
  • The system evolved for times up to $12 t_F$ (where $t_F$ is the Fermi time, the characteristic timescale of the system).
  • Time-of-Flight (ToF): At various time steps, the trap was turned off, and the atoms were imaged. A magnetic field gradient separated the host and impurity atoms spatially during expansion.
  • Data Analysis: Absorption imaging was used to reconstruct the momentum distributions $n(k)$ of both the host gas and the impurity.

3. Key Contributions

• First Experimental Observation: This is the first experimental demonstration of a microscopic quantum impurity propagating through a 1D quantum fluid without coming to a complete stop, directly challenging the macroscopic interpretation of Landau's criterion in 1D.
• Real-time Relaxation Dynamics: The study tracked the full relaxation pathway from a non-equilibrium initial state to a steady state, observing the formation of shock waves and the dressing of the impurity.
• Validation of Polaron Physics: The results confirm that the impurity forms a moving polaron state—a strongly correlated many-body state where the impurity is "dressed" by excitations of the host gas.

4. Key Results

• Supersonic Dynamics and Shock Waves:
  • For supersonic initial velocities ($Q > k_F$), the impurity rapidly transfers momentum to the host gas.
  • Within approximately one Fermi time ($t \approx t_F$), a shock wave forms, visible as a distinct momentum peak in the host gas centered at the initial impurity momentum.
  • The impurity momentum distribution splits, with a transient peak remaining at the initial $Q$ and a new peak forming near $k=0$.
• Dissipationless Steady State:
  • Contrary to the expectation that the impurity should stop ($v=0$), the impurity never comes to a complete halt.
  • After relaxation, the impurity settles into a steady state with a finite, non-zero momentum ($Q_f > 0$).
  • The final momentum $Q_f$ depends on the initial momentum $Q$ and the interaction strength $\gamma_i$. For weak interactions, $Q_f$ is linear with $Q$; for strong interactions, $Q_f$ saturates at a lower value but remains non-zero.
• Relaxation Timescales:
  • Relaxation is ultrafast, occurring on the scale of the Fermi time ($t_F$).
  • Higher initial momenta lead to faster depletion of the initial momentum peak.
• Comparison with Theory:
  • Numerical simulations based on Matrix Product States (MPS) and the Lieb-Liniger model qualitatively agree with the experimental data.
  • The steady-state momentum distribution matches the theoretical prediction for a moving polaron, which possesses an asymmetric momentum distribution due to emergent anyonic correlations in the 1D limit.

5. Significance and Implications

• Redefining Superfluidity in 1D: The work demonstrates that while Landau's criterion correctly predicts that macroscopic objects cannot move dissipationlessly in 1D, it does not apply to microscopic quantum impurities. The quantum nature of the impurity allows it to form a bound state (polaron) with the fluid that supports finite-velocity motion.
• Quantum Transport: The findings provide novel insights into how matter and information propagate in quantum many-body systems. It suggests that dissipation can be suppressed in 1D quantum fluids through the formation of correlated states.
• Future Directions:
  • The setup paves the way for observing bipolarons (bound states of two impurities).
  • It opens the door to studying quantum flutter (coherent oscillations of the impurity) and quantum Cherenkov radiation by tuning transverse confinement and interaction strengths.
  • It highlights the importance of distinguishing between macroscopic and microscopic probes when testing fundamental quantum fluid theories.

In summary, the paper resolves a long-standing theoretical debate by showing that quantum mechanics conspires to eliminate friction for microscopic impurities in 1D, allowing them to travel indefinitely at a reduced velocity as a dressed polaron, rather than stopping as classical intuition or macroscopic Landau criteria would suggest.