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arXiv:2609.14341

Engineering non-Markovianity from spectral shaping of bosonic and fermionic baths

Si Luo, Cun Long, Daochi Zhang, Massimiliano Di Ventra, Xiao Zheng

quant-phSubmitted Sep 13, 2026• Announced Sep 15, 2026• 0 citations
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Abstract

Non-Markovianity is the property that a physical system's future state depends on its previous dynamical history, namely the system has memory of its past. It is a key resource for quantum technologies but it is difficult to engineer without specific strategies. Here, we show that introducing a band gap in the environmental spectral density of both bosonic and fermionic baths provides a direct route to tuning non-Markovianity over a wide range. We demonstrate this effect by means of numerical simulations across bosonic and fermionic environments and discuss experimental tests of our predictions.

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Non-Markovianity is the property that a physical system's future state depends on its previous dynamical history, namely the system has memory of its past. It is a key resource for quantum technologies but it is difficult to engineer without specific strategies. Here, we show that introducing a band gap in the environmental spectral density of both bosonic and fermionic baths provides a direct route to tuning non-Markovianity over a wide range. We demonstrate this effect by means of numerical simulations across bosonic and fermionic environments and discuss experimental tests of our predictions.
Dissipation caused by nonhomogeneous bosonic finite chain environments (implementable in, e.g., segmented ion traps) is investigated through an exact diagonalization approach, avoiding common approximations used to describe open systems. Different spectral densities, including band gaps, can be engineered to separately assess different factors leading to memory effects, namely, the environment's size, temperature, proximity of the cutoff frequency, the spectral density's shape (sub-Ohmic, Ohmic, super-Ohmic), and the strength of its coupling to the system. Non-Markovianity is quantified with two recently introduced measures related to information backflow and nondivisibility of the system dynamical map. By sweeping the bath spectrum via tuning of the system frequency we show strongest memory effects at band-gap edges and provide an interpretation based on energy flow between system and environment. A system weakly coupled to a stiff chain ensures a Markovian dynamics, while the size of the environment as well as the local density of modes are not substantial factors. We show an opposite effect when increasing the temperature inside or outside the spectral band gap. Further, non-Markovianity arises for larger (negative and positive) powers of algebraic spectral densities, being the Ohmic case not always the most Markovian one.
We quantitatively investigate the physical origins of the non-Markovianity measure proposed in our previous work, which can be directly interpreted as memory effects, i.e., the dependence of a quantum system's future evolution on its history. Using the properties of the trace norm and the trace distance, we find that the strength of memory effects in an evolution is upper (lower) bounded by the sum (difference) of two quantities. One originates from (bounded by) the change of environment state caused by the system, the other from (bounded by) the correlations between the system and the environment. The simulation results for the Jaynes-Cummings model show that the two origins may contribute to the memory effects in different manners, depending on the initial states of the environment and the system.
We present a general theory of non-Markovian dynamics for open systems of noninteracting fermions (bosons) linearly coupled to thermal environments of noninteracting fermions (bosons). We explore the non-Markovian dynamics by connecting the exact master equations with the nonequilibirum Green's functions. Environmental backactions are fully taken into account. The non-Markovian dynamics consists of nonexponential decays and dissipationless oscillations. Nonexponential decays are induced by the discontinuity in the imaginary part of the self-energy corrections. Dissipationless oscillations arise from band gaps or the finite band structure of spectral densities. The exact analytic solutions for various non-Markovian thermal environments show that non-Markovian dynamics can be largely understood from the environmental-modified spectra of open systems.
Decoherence-free states have been found in Markovian open system dynamics and in the framework of non-Markovian fermionic environments. In the latter scenario we determine an energy range where quantum coherence is maintained over long times for every initial coherent configuration. In particular, for a two-state fermionic system interacting with a non-Markovian fermionic environment, undamped oscillating or stable coherence between the two energy eigenstates appears if the degenerate energy level is below a critical energy. If these energies coincide, the same behavior is observed in the superohmic regime and, under special conditions, the initial coherence is approached asymptotically. Equivalently, coherence persists if a defined dressed energy of the system is less than the band-gap energy of the reservoir. Same properties are found in the framework of bosonic environments.
In non-Markovian systems, the current state of the system depends on the full or partial history of its past evolution. Owing to these time correlations, non-Markovian noise violates common assumptions in gate characterization protocols such as randomized benchmarking and gate-set tomography. Here, we perform a case study of the effects of a quantum non-Markovian bath on qubit randomized benchmarking experiments. We consider a model consisting of qubits coupled to a multimode bosonic bath. We apply unitary operations on the qubits, interspersed with brief interactions with the environment governed by a Hamiltonian. Allowing for non-Markovianity in the interactions leads to clear differences in the randomized benchmarking decay curves in this model, which we analyze in detail. The Markovian model’s decay is exponential as expected, whereas the model with non-Markovian interactions displays a much slower, almost polynomial, decay. We develop efficient numerical methods for this problem that we use to support our theoretical results. These results inform efforts on incorporating quantum non-Markovian noise in the characterization and benchmarking of quantum devices.
Environmental noise is a prevalent issue that hinders the widespread adoption of quantum technologies. Standard practice to mitigate noise involves minimizing the coupling between a quantum system and its environment, which is usually modeled in the Markovian regime. By moving slightly beyond this regime into the weak non-Markovian regime, we can achieve an effective coupling that is multiple orders of magnitude smaller by exploiting the environmental memory effect. To demonstrate this effect, we simulate state swapping in a Markovian and non-Markovian environment between two modes: a cavity mode initialized as a vacuum state and an atomic motional mode initialized as a displaced squeezed coherent state. To measure the quality of state swapping between environments, we calculate and compare their corresponding multi-mode fidelity for Gaussian states. We find that a non-Markovian environment has superior state swapping fidelity across the following parameters: mean phonon number, cavity decay rate, and vibrational frequency of the atomic motional mode. The fidelity is near-unit for a non-Markovian environment within the parameter ranges mentioned in the results. These results could enable enhanced quantum information exchange between a network and chain of cavity-atom nodes and contribute toward a more prevalent adoption of quantum technologies.