⚛️ quantum physics

Fast quantum-state transfer in Su-Schrieffer-Heeger chains beyond the noninteracting regime

This paper demonstrates that by introducing tunable next-nearest-neighbor hopping phases in Su-Schrieffer-Heeger chains, it is possible to overcome interaction-induced obstructions and achieve fast, high-fidelity quantum-state transfer in both mean-field and full many-body regimes.

Original authors: François Impens, David Guéry-Odelin

Published 2026-06-23

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: François Impens, David Guéry-Odelin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a long line of people (quantum particles) standing in a hallway made of two alternating rows of lockers (a Su-Schrieffer-Heeger or SSH chain). Your goal is to move a specific person from the very first locker on the left to the very last locker on the right.

In a perfect, quiet world where no one talks to anyone else, physicists already know a clever trick to do this quickly. It's like a "shortcut" that guides the person along a specific path without them getting lost or slowing down. This is called a "shortcut to adiabaticity."

The Problem: The "Chatter" of Interactions
The paper tackles what happens when the people in the hallway start talking to each other (interacting). In the quantum world, this "chatter" creates a problem. It's like if the person you are trying to move starts getting distracted by their own thoughts or the noise of the crowd. This causes a "phase shift"—a kind of internal timing error.

If you try to use the old, simple shortcut (which only works in the quiet world) while they are chatting, the person gets confused. They might arrive at the right locker, but they are "out of sync," or they might not get there at all. The more they talk (interact), the worse the error becomes.

The Solution: A Two-Handed Approach
The authors discovered that to fix this in a noisy, interactive environment, you need to upgrade your shortcut. Instead of just one control knob, you need two.

Think of the shortcut as a dance instructor guiding the person.

The Real Hand (The Original Knob): This hand keeps the person moving along the correct path, ensuring they don't wander off into the wrong row of lockers. This is the same control used in the quiet world.
The Imaginary Hand (The New Knob): This is the paper's big discovery. This second hand doesn't move the person's location; instead, it acts like a noise-canceling headphone. It specifically cancels out the "chatter" or the internal timing errors caused by the interactions.

By using both hands simultaneously, the instructor can guide the person quickly and perfectly, even while they are surrounded by a noisy crowd. The "Imaginary Hand" is actually a way of tuning the phase (the timing) of the connections between lockers, something that is possible in modern quantum experiments.

What Happens When the Crowd Gets Huge?
The authors tested this "two-handed" method with a small crowd (a few particles) and found it worked perfectly. The person arrived exactly where they needed to be, perfectly in sync.

However, when they simulated a very large crowd (the "many-body" regime), the two-handed method was still much better than the old one, but it wasn't perfect anymore. It's like the noise-canceling headphones worked great for a small group, but in a massive stadium, the sheer volume of noise created new, complex echoes that the simple headphones couldn't fully cancel.

The Final Fix: The Master Choreographer
To solve the problem in the massive crowd, the authors used a powerful computer optimization technique (Pontryagin-based optimization). Instead of following a pre-written script (the shortcut), they let the computer act as a Master Choreographer.

This Choreographer didn't just follow the "dark path" (the simple route). It looked at the entire stadium and found a completely new, complex dance routine that wove through the crowd, using the two-handed control (the real and imaginary knobs) to navigate the chaos. This allowed the person to reach the destination with near-perfect accuracy, even in the most crowded, noisy conditions.

The Main Takeaway
The paper proves that in these quantum hallways, timing is everything.

In a quiet world, you just need to know where to go.
In a noisy world, you need to know where to go and how to cancel out the noise.
The ability to tune the "phase" (the timing) of the connections is not just a fancy technical detail; it is the essential tool needed to move quantum information quickly and accurately when particles are interacting.

The authors show that by adding this extra layer of control, we can overcome the obstacles that interactions usually create, making fast and reliable quantum transport possible even in complex systems.

Technical Summary: Fast Quantum-State Transfer in Su-Schrieffer-Heeger Chains beyond the Noninteracting Regime

Problem Statement
Topological quantum systems, particularly Su-Schrieffer-Heeger (SSH) chains, offer robust platforms for quantum-state transfer (QST) due to the resilience of edge states against disorder. While "shortcuts to adiabaticity" (STA) have successfully accelerated QST in the single-particle (linear) regime using next-nearest-neighbor (NNN) hopping, extending these methods to interacting systems has proven difficult. Interactions do not merely perturb the linear transfer; they induce nonlinear phase accumulation (self-phase modulation) that disrupts the dark-state trajectory essential for high-fidelity transfer. Existing STA protocols in topological systems have largely been restricted to the linear regime, leaving a gap in understanding how to achieve fast, high-fidelity transport in experimentally relevant interacting platforms like ultracold atoms in optical lattices.

Methodology
The authors employ a multi-stage theoretical approach to address this limitation:

Mean-Field Analysis: The study begins by extending the interaction-free NNN-assisted shortcut construction to the nonlinear mean-field regime (Bose-Hubbard model). They utilize a product-state ansatz to derive the nonlinear Schrödinger equation.
Inverse Engineering with Complex Control: The authors propose an exact analytical extension of the shortcut protocol. They decompose the NNN hopping amplitudes $\rho_n(t)$ $ρ_{n} (t)$ into real and imaginary parts (two quadratures).
- The real quadrature ( $\rho^R_n$ ) is retained from the linear shortcut to cancel nonadiabatic transitions and maintain the dark-state population profile.
- The imaginary quadrature ( $\rho^I_n$ ) is introduced as a new control resource to compensate for interaction-induced self-phase modulation.
Many-Body Benchmarking: The performance of this mean-field shortcut is tested against the full Bose-Hubbard dynamics for multiple bosons ( $M=2$ to $6$) to assess the validity of the product-state approximation.
Pontryagin Maximum Principle (PMP) Optimization: To address genuine many-body correlations beyond the mean-field picture, the authors apply PMP-based optimal control directly in the full many-body Hilbert space. This optimization relaxes the constraint of following the instantaneous dark-state trajectory, allowing the system to explore other pathways in the Fock space. The optimization is performed with both real-valued and complex-valued (phase-tunable) NNN controls.

Key Contributions

Exact Nonlinear Shortcut in Mean-Field Regime: The paper derives an exact analytical solution for fast QST in interacting SSH chains within the mean-field approximation. It demonstrates that the obstruction caused by nonlinear phase accumulation can be removed by adding a second, phase-tunable quadrature to the NNN hoppings.
Decoupled Control Mechanisms: The authors show that the two NNN quadratures play distinct, decoupled roles: the real part suppresses nonadiabatic transitions (speed-dependent), while the imaginary part cancels interaction-induced phase shifts (interaction-strength dependent). This construction is nonperturbative in the interaction strength.
Limitations of Mean-Field in Many-Body Systems: The study benchmarks the mean-field shortcut against full many-body dynamics. While the complex shortcut significantly outperforms real-valued shortcuts, it saturates below unit fidelity for $M > 1$ . This reveals that genuine many-body correlations and depletion, absent in the product-state picture, prevent the mean-field shortcut from achieving perfect transfer.
Restoration of High Fidelity via Many-Body Optimization: By optimizing directly in the many-body Hilbert space using PMP with complex, phase-tunable NNN controls, the authors recover near-perfect fidelity ( $F \approx 0.995$ ) for two-boson systems. This confirms that the imaginary NNN component is a crucial control resource even beyond the mean-field regime.

Results

Mean-Field Performance: In the mean-field regime, the protocol with both real and imaginary NNN quadratures achieves near-perfect transfer ( $1-F \le 10^{-7}$ ), effectively restoring the dark-state trajectory despite interactions. In contrast, using only real-valued NNN couplings results in degraded fidelities ( $F \approx 0.91$ for simple chains, $F \approx 0.84$ for topological interfaces).
Many-Body Performance:
- For the full Bose-Hubbard dynamics, the mean-field shortcut improves fidelity over the real-valued shortcut but saturates below unity (e.g., $F \approx 0.856$ for $M=6$ in a 9-site chain).
- PMP optimization restricted to real-valued NNN controls saturates at $F \approx 0.855$ .
- PMP optimization with complex-valued NNN controls (both real and imaginary quadratures) achieves $F \approx 0.995$ for two bosons in a 19-site topological interface chain.
Scaling and Symmetry: The real quadrature scales as $1/T$ (vanishing in the adiabatic limit), whereas the imaginary quadrature scales with the interaction strength $g$ and is independent of the transfer time scaling factor, highlighting its role as an interaction-compensating resource. The optimized controls exhibit mirror symmetry consistent with the underlying adiabatic passage.

Significance and Claims
The paper claims that hopping phases are not merely a technical refinement but a key control resource for fast and high-fidelity transport in interacting topological systems. The work establishes that:

Interactions do not inherently degrade transfer fidelity if the control manifold is sufficiently enlarged; specifically, adding an orthogonal (imaginary) quadrature to NNN hoppings allows for the exact compensation of interaction-induced phase shifts in the mean-field regime.
In the genuine many-body regime, where mean-field approximations fail to capture correlations, high-fidelity transfer can still be recovered by optimizing over the full Hilbert space using these complex controls.
The ability to tune the phase of NNN hoppings is essential for emulating nonlinear phase dynamics and enabling robust transport in regimes where interactions cannot be neglected.

The authors conclude that their results provide a pathway to fast, high-fidelity quantum-state transfer in interacting topological chains by enlarging both the control manifold (via complex hoppings) and the set of accessible quantum pathways (via many-body optimal control).

Technical Summary: Fast Quantum-State Transfer in Su-Schrieffer-Heeger Chains beyond the Noninteracting Regime

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