Relativistic treatment needed for atom coherence in quantum computing

Jen-Tsung Hsiang of National Taiwan University of Science and Technology and Bei-Lok Hu of the University of Maryland have demonstrated that standard calculations used in quantum computing may be flawed, even when atoms move at relatively slow speeds. Their work investigates how motion affects the quantum coherence of an atom’s internal degrees of freedom, revealing significant discrepancies in non-relativistic treatments.

The researchers recommend a fully relativistic calculation based on covariance principles as the proper procedure, and a much safer one in terms of accuracy, for modeling atomic dynamics. This approach is essential for designing accurate quantum information processing schemes where maintaining atomic coherence is critical.

Relativistic Treatment Crucial for Atomic Quantum Coherence

Current models often fail to account for this effect, misrepresenting the true behavior of quantum decoherence and potentially impacting the design of quantum information processing schemes. The research highlights that the perceived thermal environment shifts for an atom in motion, a phenomenon that becomes increasingly significant as speeds approach relativistic levels. A direct comparison of fully relativistic calculations with conventional non-relativistic approximations reveals significant discrepancies even at low atomic speeds, challenging the common practice of applying relativistic “corrections” to simpler models.

These calculations demonstrate that non-relativistic approaches can produce inaccurate results, even when the atom’s velocity is a small fraction of the speed of light, suggesting a need for a fundamental shift in methodology. The study extends beyond simply identifying inaccuracies. It proposes a specific methodological recommendation for modeling atomic dynamics.

The investigation considered massive objects, including neutral atoms and Unruh-DeWitt detectors, moving at constant speed within a quantum field, examining how this motion impacts quantum coherence. The team’s findings highlight the necessity of a rigorous relativistic treatment to accurately predict and mitigate decoherence in these systems, ensuring the reliability of future quantum technologies.

Researchers quantified this effect using the variance of displacement of the internal degrees of freedom, a measure similar to the spread of a wavepacket, while accounting for both quantum and thermal effects within the ambient quantum field. This research distinguishes itself from studies focusing on spatial decoherence by concentrating on the internal degrees of freedom, a critical distinction for practical applications.

Motional decoherence presents a significant concern for high-accuracy targeting and positioning of neutral atoms in traps or optical lattices, and for the design of ion-trap quantum information processing schemes, as the interplay between an atom’s motional and internal states directly impacts performance. A fully relativistic treatment is now shown to be essential for accurate modeling.

The team’s work demonstrates that temperature, being non-covariant, introduces a frame-dependent element to thermal fields, necessitating careful consideration of the frame where fluctuations appear homogeneous. A key finding details the origins of inaccuracies in non-relativistic calculations that attempt to incorporate relativistic “corrections”. The calculations use = to measure the decoherence dynamics of the internal degree of freedom due to the atom’s external motion.

Quantum Dispersion and Motional Decoherence of Internal States

The variance of an atom’s internal degree of freedom is a quantifiable measure of quantum dispersion, even when the atom is stationary, and motional decoherence when in motion, according to new calculations. This metric, analogous to the spread of a wavepacket, allows for precise assessment of how external quantum fields impact an atom’s internal state, a critical consideration for advanced quantum technologies. Researchers distinguish this focus on internal decoherence from more common studies of spatial decoherence, which examine changes to an atom’s external wave function.

Variance Measurement of Internal Degree of Freedom Wavefunctions

The equation governing the internal dynamics of an atom, when considered along its inertial worldline, reveals a specific form dependent on a damping constant γ = λ^2/(8π m), where λ and m represent intrinsic atomic properties. This equation, χ(τ) + 2γ χ(τ) + ${\omega }^2\chi (\tau )$ = λ/m ${\phi }_h(z^{\mu }(\tau ))$, dictates how the internal degree of freedom evolves under the influence of a quantum field, ${\phi }_h$. The proper procedure, and a much safer one in terms of accuracy, is recommended here: first derive the dynamics and the necessary regularizations within a fully covariant relativistic framework.

Only after the exact, internally consistent equations of motion are established should low-velocity limits be extracted from them. Only in this way can all the relativistic effects which matter, time dilation, aberration, non-inertial mass shifts, be systematically preserved, and accurate results obtained.

Vacuum Fluctuations Drive Potential Vacuum Viscosity Effects

Ignoring the time dilation experienced by an atom’s internal degrees of freedom is justifiable only at very low velocities, according to new calculations detailing the impact of vacuum fluctuations on quantum coherence. While commonly accepted approaches approximate atomic dynamics using non-relativistic quantum mechanics, these methods overlook subtle effects that become significant even at speeds far below those encountered in typical laboratory settings. The work suggests existing designs for quantum information processing may be flawed due to these overlooked relativistic effects.

These discrepancies stem from a failure to account for the proper time experienced by the atom’s internal state, rather than relying on laboratory time measurements. The researchers write, but emphasize that even small velocities introduce errors. The work aims to explore the root cause of quantum friction, a phenomenon still poorly understood, and will investigate the mechanical degree of freedom, specifically the center of mass of the atom.

AMOF Model Links Atom’s Internal and Mechanical Degrees

The AMOF model reveals a velocity-dependent decoherence stemming from an artificial breakdown of Lorentz covariance, a result not predicted by standard calculations. The research shows that at zero temperature, the decoherence measure is independent of the atom’s velocity, establishing that uniform motion through the quantum vacuum does not alter the decoherence dynamics of the internal degrees of freedom.

This stands in stark contrast to results obtained from non-relativistic formulations, which predict a significant velocity dependence. The team’s analysis, using a model linking the atom’s center-of-mass motion to its internal structure, shows that the proper treatment requires formulating the internal dynamics in a fully relativistic manner.

Non-Relativistic Approaches Introduce Fictitious Friction

Non-relativistic quantum mechanics, a nearly standard practice in atomic, molecular and optical (AMO) physics, can introduce artificial friction into calculations of atomic internal dynamics, according to new work focused on quantum coherence. This spurious friction arises from violations of Lorentz invariance when relativistic “corrections” are applied to non-relativistic calculations, potentially skewing results even at low atomic speeds.

The research highlights a critical need for fully relativistic treatments when modeling interactions between moving atoms and quantum fields. The investigation centers on obtaining accurate predictions of decoherence, the loss of quantum information, in an atom’s internal degrees of freedom, a key concern for designing robust quantum information processing schemes.

They demonstrate that simply adding relativistic adjustments to existing non-relativistic models is insufficient, and can lead to physically unrealistic outcomes. “Describing the idf dynamics with nonrelativistic quantum mechanics is almost standard in atomic-molecular-optical (AMO) physics, but the violation of Lorentz invariance in any kind of hybrid treatments could lead to nonphysical effects such as the appearance of fictitious friction,” the researchers write. The study advocates for a fundamentally different approach: deriving dynamics and regularizations within a fully covariant relativistic framework before extracting low-velocity limits.

Selective application of the Doppler shift, a common technique to account for atomic motion, also proves problematic. The research emphasizes that relativistic corrections must emerge self-consistently from the underlying field theory, rather than being selectively imposed on a non-relativistic foundation.

Lorentz Invariance Essential for Accurate Internal Dynamics

A breakdown of Lorentz covariance within models of atomic motion artificially amplifies decoherence, even at speeds considered low for quantum computing applications, new calculations reveal. This inconsistency arises when internal atomic dynamics are not formulated using fully relativistic principles, leading to predictions that diverge from those expected under Lorentz invariance. The research demonstrates that non-relativistic treatments, despite their widespread use in atomic-molecular-optical physics, introduce spurious effects like fictitious friction and inaccurate decoherence rates.

Comparing fully relativistic and non-relativistic calculations, the team found significant discrepancies in the latter, even when atomic velocities are small. Specifically, a non-relativistic model incorrectly predicts monotonically increasing decoherence with rising velocity, a result absent in the Lorentz-invariant relativistic calculation. This effect stems from relativistic time dilation and is particularly pronounced when approximating the quantum field as a vacuum, effectively ignoring the inherent consistency demanded by covariance principles.

The team’s analysis focused on the quantum noise originating from fluctuations of quantum fields at zero temperature, distinguishing it from the better-understood Einstein-Hopf drag associated with thermal fields. The study highlights that a thermal field, by defining a preferred rest frame, inherently breaks Lorentz invariance, a contrast to the Minkowski vacuum’s independence from velocity at zero temperature. However, the researchers found that when a non-relativistic approach is used, an unusually strong velocity-dependent decoherence emerges, indicating a fundamental flaw in the methodology.

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