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Physical review. B./Physical review. B

Transport in open quantum systems in the presence of lossy channels

Katha Ganguly, Manas Kulkarni, Bijay Kumar Agarwalla

Published Dec 24, 2024• 11 citations
Publisher

Abstract

We study nonequilibrium steady-state transport in a boundary driven one-dimensional fermionic lattice setup which is further subjected to particle loss. We analyze the system size scaling of conductance at zero temperature for different values of the chemical potential of the boundary reservoirs. We consider a variety of loss channel configurations: (i) single loss at the middle site of the lattice, (ii) multiple but nonextensive lossy channels, and (iii) extensive lossy channels. For the cases (i) and (ii), the conductance scaling with system size remains robust (i.e., same as the case with no loss) for chemical potential within and outside the lattice band, while at the band edge rich anomalous conductance scaling emerges. For case (iii), the conductance scaling becomes ballistic in the thermodynamic limit for any value of chemical potential. We explain the emergence of these different system size scalings of conductance by analyzing the spectral properties of the associated non-Hermitian transfer matrices of the underlying lattice. We demonstrate that the emergence of anomalous scaling is deeply connected to the existence of exceptional points of transfer matrices. Our study unravels that by carefully optimizing the loss mechanism configurations, one can in principle realize systems with rich transport properties in low-dimensional open quantum systems.

DOI
10.1103/physrevb.110.235425

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We study nonequilibrium steady-state transport in a boundary driven one-dimensional fermionic lattice setup which is further subjected to particle loss. We analyze the system size scaling of conductance at zero temperature for different values of the chemical potential of the boundary reservoirs. We consider a variety of loss channel configurations: (i) single loss at the middle site of the lattice, (ii) multiple but nonextensive lossy channels, and (iii) extensive lossy channels. For the cases (i) and (ii), the conductance scaling with system size remains robust (i.e., same as the case with no loss) for chemical potential within and outside the lattice band, while at the band edge rich anomalous conductance scaling emerges. For case (iii), the conductance scaling becomes ballistic in the thermodynamic limit for any value of chemical potential. We explain the emergence of these different system size scalings of conductance by analyzing the spectral properties of the associated non-Hermitian transfer matrices of the underlying lattice. We demonstrate that the emergence of anomalous scaling is deeply connected to the existence of exceptional points of transfer matrices. Our study unravels that by carefully optimizing the loss mechanism configurations, one can in principle realize systems with rich transport properties in low-dimensional open quantum systems.
Quasiperiodic systems host exotic transport regimes that are distinct from those found in periodic or disordered lattices. In this work, we study quantum transport in the Aubry-André-Harper lattice in a two-terminal setup coupled to zero-temperature reservoirs, where the conductance is evaluated via the nonequilibrium Green's function method. In the extended phase, we uncover a universal subdiffusive transport when the bath chemical potential aligns with the band edges. Specifically, the typical conductance displays a scaling of Gtyp∼L−2\mathcal{G}_{\text{typ}}\sim L^{-2}Gtyp​∼L−2 with system size LLL. We attribute this behavior to the emergence of an exceptional point (Jordan normal form) in the transfer matrix in the thermodynamic limit. In the localized phase, the conductance shows exponential decay governed by the Lyapunov exponent. Intriguingly, in the critical phase, we identify pronounced log-periodic oscillations of the conductance as a function of system size, arising from the discrete scale invariance inherent to the singular-continuous spectrum. We further extend our analysis to the generalized Aubry-André-Harper model and provide numerical evidence suggesting that the exact mobility edge resides within a finite spectral gap. This results in a counter-intuitive exponential suppression of conductance precisely at the mobility edge. Our work highlights the distinct transport behaviors in quasiperiodic systems and elucidates how they are rigorously dictated by the underlying local spectral structure.
We show that a one-dimensional ordered fermionic lattice system with power-law-decaying hopping, when connected to two baths at its two ends with different chemical potentials at zero temperature, features two phases showing subdiffusive scaling of conductance with system size. These phases have no analogues in the isolated system (i.e., in absence of the baths) where the transport is perfectly ballistic. In the open system scenario, interestingly, there occurs two chemical-potential-driven subdiffusive to ballistic phase transitions at zero temperature. We discuss how these phase transitions, to our knowledge, are different from all the known nonequilibrium quantum phase transitions. We provide a clear understanding of the microscopic origin of these phases and argue that the subdiffusive phases are robust against the presence of arbitrary number-conserving many-body interactions in the system. These phases showing subdiffusive scaling of conductance with system size in a two-terminal setup are therefore universal properties of all ordered one-dimensional number-conserving fermionic systems with power-law-decaying hopping at zero temperature.
We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $\ensuremath{\alpha}$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a nonequilibrium steady-state charge transport, and (ii) time dynamics of an initially localized single-particle excitation in the absence of boundary reservoirs. In both variants, anomalous superdiffusive behavior is observed for $1<\ensuremath{\alpha}<1.5$, and for $\ensuremath{\alpha}>1.5$ the setup is effectively short ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behavior in open quantum systems.
We characterize the particle transport, particle loss, and nonequilibrium steady states in a dissipative one-dimensional lattice connected to reservoirs at both ends. The free-fermion reservoirs are fixed at different chemical potentials, giving rise to particle transport. The dissipation is due to a local particle loss acting on the center site. We compute the conserved current and loss current as functions of voltage in the nonlinear regime using a Keldysh description. The currents show steplike features that are affected differently by the local loss: the steps are either smoothened, nearly unaffected, or even enhanced, depending on the spatial symmetry of the single-particle eigenstate giving rise to the step. Additionally, we compute the particle density and momentum distributions in the chain. At a finite voltage, two Fermi momenta can occur, connected to different wavelengths of Friedel oscillations on either side of the lossy site. We find that the wavelengths are determined by the chemical potentials in the reservoirs rather than the average density in the lattice.
Recently, it has been shown that, in one-dimensional fermionic systems, close to band edges, the zero temperature conductance scales as 1/N21/{N}^{2}1/N2, where NNN is the system length. This universal subdiffusive scaling of conductance at band edges has been tied to an exceptional point (EP) of the transfer matrix of the system that occurs at every band edge. Further, in the presence of bulk dephasing probes, this EP has been shown to lead to a counterintuitive superballistic scaling of conductance, where the conductance increases with NNN over a finite but large regime of system lengths. In this work, we explore how these behaviors are affected by the order of the transfer matrix EP at the band edge. We consider a one-dimensional fermionic lattice chain with a finite range of hopping. Depending on the range of hopping and the hopping parameters, this system can feature band edges which correspond to arbitrarily higher order EPs of the associated transfer matrix. Using this system we establish in generality that, in the absence of bulk dephasing, surprisingly, the universal 1/N21/{N}^{2}1/N2 scaling of conductance is completely unaffected by the order of the EP. This is despite the fact that existence of transfer matrix EP is crucial for such behavior. In the presence of bulk dephasing, however, the phase coherence length, the extent of the superballisitic scaling regime, and the exponent of superballistic scaling all encode the order of the transfer matrix EP.
One of the major advances of quantum technology is the engineering of complex quantum channels in lattice systems that paves the way for a variety of novel non-equilibrium phenomena. For a boundary driven lattice with such engineered quantum channels, the analysis of the full counting statistics of current across boundaries has received limited attention. In this work, we consider a boundary driven free fermionic lattice with carefully engineered correlated gain and loss channels and obtain the cumulant generating function of the steady-state particle current. We also discuss the limit for simplifying the correlated gain-loss channel to a local gain-loss channel and obtain the average current and its fluctuation in such cases. Generally, in the presence of gain-loss, the current statistics are different at the two ends of the lattice. Hence, for both local and correlated gain-loss, we devise the conditions for which the statistics can coincide, giving rise to a PT\mathcal{PT}PT symmetric balanced gain-loss scenario. A striking difference between the correlated gain-loss and their local counterpart is the emergence of nonreciprocity in the system and we observe that it has a dramatic impact in the current as well as fluctuations. Our work therefore provides interesting insights about the importance of engineered dissipators in boundary driven systems.