Two qubits now map how energy spreads through quantum systems

Hossein Hosseinabadi of Johannes Gutenberg-Universität Mainz and colleagues have demonstrated that a two-qubit quantum sensor can map how energy spreads through complex quantum systems, separating the response and noise of the environment being probed, a capability extending beyond single-qubit sensing. The work reveals that this approach resolves the spatio-temporal spreading of correlations, visualizing the dispersion of low-energy excitations as light-cone-like profiles. Researchers further found that external driving can modify this profile, creating additional fringes outside the light-cone, and that the method distinguishes between different energy transport regimes including ballistic spreading and diffusive broadening.

Two-Qubit T₂ Spectroscopy Measures Many-Body System Dynamics

A two-qubit sensor can distinguish between ballistic, diffusive and crossover transport regimes within a quantum system, offering a new level of granularity in observing energy movement. The method relies on a T₂ spectroscopy framework, allowing this approach to resolve the spatio-temporal spreading of correlations in a many-body system. The study considered a many-body system coupled to two qubits, employing pulse protocols designed to separately access symmetric and antisymmetric correlation functions.

“Many-body systems display a wide variety of dissipative behaviors, including those covered by the Hohenberg-Halperin classification according to their conservation laws,” the paper notes, highlighting the broad applicability of the technique to diverse quantum systems. The researchers suggest that future work will explore the potential of this two-qubit spectroscopy in even more complex scenarios, expanding its utility for characterizing quantum materials and processes.

Correlated Noise Extraction via Two-Qubit Pulse Sequences

A two-qubit sensing architecture now independently extracts environmental noise and the system’s response, a capability particularly valuable when systems are not in thermal equilibrium. This separation is achieved through specifically designed pulse sequences within a T₂ spectroscopy framework, moving beyond the limitations of single-qubit measurements. The technique allows researchers to dissect the contributions of disturbance and reaction within the probed environment, even when standard relationships between fluctuations and dissipation break down.

This approach can resolve the spatio-temporal spreading of correlations in a many-body system and clearly distinguishes between different transport regimes in the system, including ballistic spreading, diffusive broadening and the transitions between them. “By selecting appropriate pulse protocols, the two-qubit architecture separately extracts the symmetric (noise) and antisymmetric (response) correlation functions of the environment,” the study notes. This advancement allows for a more complete understanding of the system’s behavior, particularly in scenarios where traditional methods struggle.

The researchers suggest that extending these results to more complex pulse protocols will further refine the ability to probe specific energy scales and improve the sensitivity of the measurements. This refined control over pulse sequences promises even greater insight into the complex dynamics of many-body quantum systems.

Light-Cone Profiles Reveal Correlation Propagation Speed

The resulting correlated dephasing signal provides a new method for characterizing many-body dynamics, offering insights previously inaccessible. Initial demonstrations of correlated fluctuations in individual measurements were achieved using nitrogen-vacancy centers subjected to artificial noise, theoretically predicting the ability to reveal spatial structure and non-Gaussian noise. This work builds on that foundation, demonstrating that a two-qubit implementation of correlation T₂ spectroscopy provides real-time and real-space access to the propagation of correlations.

These correlations manifest as a light-cone structure in the correlated dephasing signal, vanishing at distances exceeding the product of the correlation speed and elapsed time. This behavior directly reflects how correlations spread within the many-body system, confirming theoretical predictions about the dispersion of excitations. The observed light-cone profiles were established through analysis of the integrated response, which displayed a similar behavior with a smaller amplitude. The researchers noted, indicating future work will expand on this framework.

Non-Equilibrium Effects on Correlation Spreading

The ability to discern how energy propagates through complex quantum systems now extends beyond predictions of equilibrium, as a two-qubit spectroscopy method reveals modifications to correlation spreading under non-equilibrium conditions. Analysis of the resulting correlated dephasing signal demonstrates that external driving can produce additional fringes extending beyond the expected light-cone profile, a deviation from standard energy dispersal patterns. These fringes indicate a reshaping of the interaction landscape when the probed many-body system is not in thermal equilibrium, offering a new way to characterize its dynamic state.

The foundation for this observation lies in the initial state preparation, where the density matrix of the qubits and the many-body system is established, potentially starting from a state not at thermal equilibrium. The team’s calculations show that the symmetric correlation function of a key operator, $B_k$, directly influences the mode occupation, $n_k$ and ultimately the observed correlations.

This is particularly evident when low-momentum modes are excited, leading to long-range fringes in the correlated dephasing signal that surpass the boundaries of the typical equilibrium light-cone. In contrast, driving modes at finite momenta introduces a spatial modulation to this fringe pattern, further highlighting the sensitivity of the method to non-equilibrium excitations.

This two-qubit approach builds on established techniques like two-dimensional spectroscopy, but offers a streamlined method for accessing linear response and correlation functions within the many-body environment. The analysis relies on calculating the correlated dephasing and integrated response, derived from the equations of motion for operators $B_k$ and ${\pi }_k$, with the resulting expression for the Ramsey component of the signal, $X_{12}^{Ram}(t)$, revealing the spatial dependence of the correlations.

The team notes that while they focused on Ramsey and spin echo pulse sequences, the framework is readily extensible to more sophisticated protocols, potentially unlocking even richer insights into the system’s dynamics. “We have shown that the simplest two-qubit setup already provides access to the linear response and correlation functions of the many-body environment,” the researchers state, indicating future work will explore these more complex pulse sequences.

Distinguishing Transport Regimes with Correlated Dephasing

A two-qubit sensor architecture independently extracts the noise and response of a probed environment, offering a refinement over single-qubit sensing techniques. This separation is particularly valuable when examining systems not in thermal equilibrium, where standard relationships between fluctuations and dissipation no longer hold true, as the two-qubit setup accesses both symmetric and antisymmetric correlation functions.

Visualizing the propagation of these correlations reveals how fluctuations spread through space and time, providing insight into the dispersion of low-energy collective modes within the quantum system. The method’s sensitivity extends to quantifying these regimes; for example, the diffusion length, a measure of how far particles spread, can be extracted from the asymptotic form of the correlated dephasing signal.

Quantum Sensing Extends Beyond Single-Qubit Limitations

This advancement allows for a unified framework applicable to both engineered quantum systems and solid-state defect probes, offering new insights into complex quantum dynamics. Researchers are no longer limited to traditional T₁ and T₂ spectroscopies, but can now employ multi-qubit sensors to reveal previously inaccessible information about environmental noise. This approach opens avenues for both quantum simulation and quantum information processing, particularly relevant to experiments scaling up protocols with nitrogen-vacancy centers.

The availability of multiple qubits facilitates entanglement through fluctuations in the host material, a key step toward more complex quantum operations. Further exploration of these systems involves introducing additional evolution windows between pulses or incorporating more than two qubits, enabling access to higher-order correlations and responses beyond Gaussian statistics. “Recent experiments, especially with NV centers, are scaling up the protocol of Ref.,” the authors note, indicating future directions for this technology.

Solid-State Defects and Quantum Coherent Probes

This differentiation stems from a new approach to T₂ spectroscopy, where carefully designed pulse sequences applied to a two-qubit sensor separately extract the response and noise of the probed environment. This technique extends beyond simply detecting the presence of noise, allowing researchers to characterize its specific behavior and how it propagates through a material. The method reveals the spatial structure of these correlations through light-cone-like profiles, visually demonstrating the dispersion of low-energy excitations within the many-body system.

These profiles directly illustrate how energy and information spread, providing a real-space map of the system’s dynamics. Theoretical work suggests this approach can reveal momentum-resolved noise, offering even greater insight into the underlying mechanisms governing these interactions. The ability to map these correlations in both space and time represents an advancement in the field of quantum sensing, promising new avenues for exploring the behavior of complex quantum materials.

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