Single Measurement Steers Atoms to Stable Dark States

Scientists are increasingly focused on preparing subradiant states in collectively emitting two-level emitters, a process complicated by their inherently weak interactions. Ipsita Bar, Aditi Thakar, and B. Prasanna Venkatesh, all from the Indian Institute of Technology Gandhinagar, demonstrate a novel platform-independent protocol utilising projective measurements on a single two-level emitter to overcome these limitations. Their research reveals that a single measurement can significantly populate single-excitation subradiant steady states in permutation-symmetric ensembles and drive generic arrays towards a nearly pure state exhibiting substantial overlap with the subradiant Dicke subspace. This work represents a significant advance as it bypasses the need for complex patterned driving, local control, or structured environments, offering a potentially simpler route to harnessing subradiance for applications in quantum information processing and low-light technologies.

Future optical devices could become far more efficient, manipulating light with exquisite precision. Achieving this requires controlling the collective behaviour of many tiny light emitters, a challenge now addressed by a novel measurement technique. By observing just one emitter, scientists can steer an entire ensemble into a desirable, low-energy state, paving the way for advanced photonics.

Scientists are increasingly focused on controlling the behaviour of quantum systems to unlock advances in areas like sensing and computation. A persistent challenge lies in preparing and maintaining subradiant states within ensembles of two-level emitters (TLEs), which are quantum systems capable of emitting light at specific frequencies. These states, characterised by suppressed spontaneous emission, hold promise for creating long-lived quantum memories and entanglement, yet their inherent ‘dark’ nature complicates their preparation.

Current methods often demand complex control schemes or precisely engineered environments, becoming impractical as the number of emitters increases. Researchers propose a new, platform-independent approach to generating these subradiant states, relying solely on the act of measuring a single emitter within the ensemble. Initial investigations reveal that a single, well-timed measurement can shift the collective state of permutation-symmetric ensembles towards a desired subradiant configuration.

Repeated measurements performed on one emitter can effectively steer the remaining, unmeasured emitters into a nearly pure subradiant state, exhibiting strong alignment with the subradiant Dicke subspace, a specific quantum configuration. Understanding how measurement back-action can control these systems requires careful consideration of the collective behaviour of the emitters.

Local measurements offer an irreversible way to redistribute population, steering the system away from superradiant to subradiant states. This technique bypasses the need for complex control mechanisms or specially designed structures, potentially opening doors to simpler and more scalable quantum technologies. At the heart of this process is the Monte-Carlo wavefunction (MCWF) formalism, a method for simulating the quantum evolution of many-body systems by tracking individual quantum trajectories.

The precise timing of these measurements is critical. Calculations indicate that the lifetime of the subradiant state can be extended by performing measurements at specific times, as demonstrated by simulations. For permutation-symmetric ensembles, analytical expressions and numerical solutions confirm that a single measurement of either σz or σx, Pauli operators representing specific quantum properties, yields a substantial probability of occupying a subradiant Dicke state. Also, in generic arrays lacking this symmetry, repeated measurements on one emitter effectively prepare subradiant steady states within the remaining unmeasured emitters, offering a pathway to strong quantum states across diverse experimental platforms.

Monte Carlo wavefunction modelling of collective emission and projective measurement

A detailed examination of collective spontaneous emission utilised the Monte-Carlo wavefunction (MCWF) quantum trajectory evolution formalism to model the behaviour of two-level emitters. This approach allows tracking the probabilistic evolution of quantum states, essential for understanding the impact of measurement on the system. Following initial excitation, the system’s progression was simulated, accounting for collective decay and the subsequent influence of local projective measurements.

These measurements, performed on a single emitter, project the system into specific states, steering it towards subradiant configurations. The research began by defining N two-level emitters, each with an energy gap ω0 and arranged to interact collectively within a shared electromagnetic environment. By employing the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, the evolution of the system’s density matrix ρ was calculated, incorporating both coherent interactions and spontaneous emission.

This equation accounts for dipole-dipole interactions (Ωlm) and correlated decay rates (Γlm), providing a complete description of the collective dynamics. The core of the methodology lies in the implementation of local quantum measurements. At a specific time tm, a projective measurement of either the σz or σx observable was applied to a single emitter.

The choice of these Pauli operators allows probing different aspects of the emitter’s excitation state. The study then calculated the steady-state occupation probability P ss sub, representing the fraction of quantum trajectories ending in a subradiant Dicke state |J, M, α>. For generic arrays lacking permutation symmetry, repeated measurements were performed on one emitter, and the population dynamics within the subradiant Dicke states of the remaining N-1 emitters were tracked. This technique relies solely on measurement back-action, offering a minimal resource for generating subradiant many-body states and is directly applicable across diverse experimental platforms.

Subradiant population transfer and measurement-time scaling in symmetric emitter ensembles

For permutation-symmetric ensembles of two-level emitters, a single measurement of σz yields a subradiant population of up to 0.4, representing the fraction of the collective excitation residing within the subradiant Dicke subspace after the measurement is performed at an optimal time. Calculations, corroborated by direct numerical simulation, demonstrate this significant population transfer is achievable by carefully timing the measurement.

Measurements of σx exhibit reciprocal behaviour, reaching 50% population in the dark steady-state with a single measurement either early or late in the evolution, with a minimum at an intermediate time. The optimal measurement time, denoted t⋆m, scales logarithmically with the number of emitters N, specifically as Γ0t⋆m ∼ log(N)/N, mirroring the peak radiation rate observed in superradiant emission.

Extending this analysis beyond perfectly symmetric systems, the research considers arrays of identical emitters arranged along a one-dimensional waveguide. A single measurement does not establish a steady-state subradiant population, due to the absence of permutation symmetry. The ratio of the spontaneous lifetime with measurement, tsub, to that without measurement, tum sub, provides a measure of enhancement.

Examining arrays of seven emitters separated by 0.34λ0 within a waveguide, repeated measurements of σx on a single emitter at a rate rm demonstrate the possibility of achieving a finite steady-state subradiant population, P N−1 sub, for the remaining unmeasured emitters. For a measurement rate of 0.25Γ0, the subradiant population reaches a steady value, confirmed by the presence of a finite number of excitations within the unmeasured portion of the array.

By deriving an effective master equation within the Zeno limit, the study reveals the evolution of the reduced density matrix for the unmeasured emitters, denoted χ, and its components in the Zeno subspace. This evolution is governed by an effective Hamiltonian H′ and a Lindblad term LN−1, alongside a decay rate of Γ0/4, in the end demonstrating the potential for sustained subradiant states through continuous measurement.

Steering quantum many-body systems via selective projective measurements

Scientists have long sought methods to control collective behaviour in systems of many interacting quantum particles, yet achieving stable, predictable states remains a considerable challenge. This research presents a way to steer these ensembles towards desired configurations, bypassing direct manipulation. Rather than forcing order through external controls, the team demonstrates a way to ‘guide’ the system using only single-particle observations.

Previous attempts relied on precise patterning or strong local driving, both of which introduce practical limitations and scaling problems. By cleverly applying projective measurements, researchers can effectively prune away unwanted states, concentrating the system’s probability onto a subradiant configuration. This approach is independent of the specific platform used to realise these emitters, offering a degree of generality absent in many existing techniques.

The method isn’t without its constraints. Although simulations suggest scalability to larger numbers of emitters, the computational cost currently limits full calculations. The purity of the resulting state, while improved over strong driving, isn’t absolute, and entanglement doesn’t see as large a boost. The protocol optimises for a specific arrangement of emitters, and exploring the robustness of this preparation to deviations from ideal conditions will be important.

This work could inspire new approaches to quantum information storage and processing. Instead of building complex control systems, we might instead focus on designing measurement schemes that ‘shape’ quantum states. Beyond this specific system, the principle of measurement-induced state preparation could find applications in diverse areas, from controlling chemical reactions to manipulating complex materials. The focus will likely shift towards experimental realisation and demonstrating the practical benefits of this subtle but potentially powerful technique.