Researchers Steer Quantum States Using Engineered Loss

Appropriately designed dissipation favours either localised or extended states within a purely non-disordered one-dimensional lattice. The foundational clean lattice exhibits spatially inhomogeneous hopping and sustains both extended bulk states alongside localised boundary states, encompassing an algebraically localised bound state in the continuum. A nonlocal bond jump operator with a tunable relative phase reveals a selective preference for eigenstates characterised by differing spatial phase correlations. Consequently, the prolonged-duration density matrix is steered toward portions governed by either localised or extended Hamiltonian eigenstates without chaos.

Engineered Dissipation Enables High Fidelity Control of Quantum State Distributions Scientists at College of Mathematics and Physics, collaborating with Hangzhou Normal University, Nankai University, and Chengdu University of Technology, have demonstrated a method to steer long-time density matrix distributions. They achieved over 95 per cent transition between states dominated by either localised or extended Hamiltonian eigenstates, a level of control previously unattainable in strictly non-disordered systems.

This precise steering relies on engineered dissipation via phase-selective bond jump operators which favour specific spatial phase correlations within the lattice without altering its inherent parameters. This introduces a controllable mechanism for manipulating quantum state preparation and transport characteristics in one-dimensional lattices, offering potential advancements across diverse physical platforms like photonic architectures and ultracold atomic gases.

Manipulating dissipation, the loss of energy from a system, can actively select for either localised or extended quantum states within a lattice structure. Measurements of site pairs quantified this selection process, with the fraction demonstrating matching phases with the dissipative channel revealing the underlying microscopic origin driving state preference as represented by distance l between phase matched sites. Analysis via ‘quantum fidelity’ demonstrated that once selected, these steady-state characteristics persisted even after removing the engineered dissipation itself; this indicates strong durability beyond initial manipulation.

Achieving over 95 per cent transition between localised and extended eigenstates is important, though current results do not yet demonstrate scalability to larger systems nor address practical limitations in maintaining precise phase control required for real-world applications. The phenomenon of Anderson localization, first elucidated by P. W. Anderson in 1958, fundamentally revolutionized our understanding of wave propagation in disordered media.

It established that random potential fluctuations can exponentially localise electron waves, completely suppressing spatial diffusion and inducing a metal-insulator transition. Over subsequent decades, this seminal framework has inspired extensive investigations across diverse physical platforms, ranging from photonic architectures and acoustic materials to ultracold atomic gases.

However, localisation also occurs in non-disordered systems; this challenges the traditional model that randomness is essential for wave localisation and includes findings such as localisation in clean lattices with tailored nonlinearities or through engineered synthetic dimensions offering new pathways to control wave propagation without relying on disorder. Concurrently, the field of open quantum systems has experienced a remarkable resurgence propelled by experimental advancements in precise engineering of dissipation and system-environment dynamics.

Within this context, the interaction between environmental dissipation and wave transport has become a focal point of research. Traditionally it was thought that dissipation inherently erodes phase relationships required for localised states inevitably driving the system toward an ergodic, delocalized steady state.

Yet emerging theoretical studies suggest a more subtle role for dissipation: it can drive Anderson localization into a strong stationary state without destroying it, and induce dephasing-driven mobility edges (MEs) in quasicrystals. Furthermore, specific dissipative couplings mediate deterministic transitions between extended and localized states in one-dimensional quasiperiodic systems featuring MEs; despite these advances, a critical gap remained.

The capacity of dissipation to actively induce and control extended-to-localized transitions in strictly non-disordered systems largely unexplored. This work addresses this gap by exploring a tunable transition between extended and localized steady states in a non-disordered lattice driven entirely by engineered bond dissipation.

Phase-selective dissipative jump operators were constructed to demonstrate precise, deterministic control over asymptotic states and transport characteristics of the open system. The team systematically investigated the steady-state density matrix distributions in both real-space and eigenstate representations tracking corresponding dynamical evolution.

Their findings reveal that irrespective of initial preparation, the system can be robustly steered into a stationary regime dominated by either extended or localized modes; crucially, this transition is governed by experimentally accessible parameters, the relative phase α and inter-site distance l. This establishes non-local bond dissipation as a flexible set of tools for tuning localisation transitions offering new theoretical perspectives on quantum state manipulation in open disorder-free architectures.

The methodology detailed within this paper begins with Section II defining the non-disordered tight-binding model featuring inhomogeneous hopping rates sustaining bound states in the continuum. Subsequently, Section III describes the open-system dynamics using the Lindblad master equation equipped with phase-dependent bond dissipator. Numerical results concerning dissipation-tunable extended and localised steady states are analysed and discussed in Section IV; finally, Section V provides a thorough summary of findings considering a strictly disorder-free one-dimensional (1D) tight-binding lattice with spatially modulated nearest neighbour hopping amplitudes.

This boundary condition in the continuum exhibits structural durability against alterations to lattice parameters, as detailed later.

To examine nonunitary dynamics and the emergence of steady states within this disorder-free system, a problem involving an open quantum system governed by a Lindblad master equation is formulated. Here, Oj is a jump operator for the jth dissipative channel and Γ signifies the overall dissipation rate; these terms describe reversible coherent evolution alongside irreversible coupling with a Markovian environment.

Engineered dissipation can select localised or extended states in strictly non-disordered one-dimensional lattices possessing spatially inhomogeneous hopping and both bulk plus boundary states. Dissipation is usually regarded as a source of decoherence that suppresses quantum interference and localization. The underlying clean lattice has spatially inhomogeneous hopping and supports both extended bulk states and localised boundary states, including an algebraically localised bound state within the continuous spectrum.

A nonlocal bond jump operator with a tunable relative phase selectively favours eigenstates possessing differing spatial phase correlations. Consequently, the long-time density matrix steers towards sectors dominated by Hamiltonian eigenstates that are either localised or extended; no alteration to any Hamiltonian parameter is required for this process. The microscopic origin of this selection is quantified by assessing the fraction of site pairs separated by distance l which exhibit phase matching with the dissipative channel.

Characterisation of the dissipative quench via quantum fidelity reveals that selected steady-state characteristics persist even after dissipation ceases, these findings establish phase-selective bond dissipation as a method for controllable state preparation and manipulation of transport in non-disordered lattices. This clean lattice supports both extended bulk states and localised boundary states, including an algebraically localised bound state within the continuous spectrum.

A nonlocal bond jump operator with a tunable relative phase selectively favours eigenstates possessing differing spatial phase correlations.

Researchers demonstrated that engineered dissipation can select between localised and extended states within a one-dimensional lattice without introducing disorder. This control arises from manipulating spatial phase correlations using a nonlocal bond jump operator, allowing steering towards specific Hamiltonian eigenstates. Analysis utilising quantum fidelity showed that this selection persists once the dissipation is removed, indicating stable state preparation. The fraction of site pairs separated by distance l exhibiting matching phases quantified how this process functions.