Controlling phase transitions in quantum systems via coupling to reservoirs has been mostly studied for idealized memory-less environments under the so-called Markov approximation. Yet, most quantum materials and experiments in the solid state, atomic, molecular and optical physics are coupled to reservoirs with finite memory times. Here, using the spectral theory of non-Markovian dissipative phase transitions developed in the companion paper [Debecker et al., Phys. Rev. A 110, 042201 (2024)], we show that memory effects can be leveraged to reshape matter phase boundaries, but also reveal the existence of dissipative phase transitions genuinely triggered by non-Markovian effects.Controlling phase transitions in quantum systems via coupling to reservoirs has been mostly studied for idealized memory-less environments under the so-called Markov approximation. Yet, most quantum materials and experiments in the solid state, atomic, molecular and optical physics are coupled to reservoirs with finite memory times. Here, using the spectral theory of non-Markovian dissipative phase transitions developed in the companion paper [Debecker et al., Phys. Rev. A 110, 042201 (2024)], we show that memory effects can be leveraged to reshape matter phase boundaries, but also reveal the existence of dissipative phase transitions genuinely triggered by non-Markovian effects.

arXiv:2307.01119Jul 3, 20230 citations

Spectral theory of non-Markovian dissipative phase transitions

Baptiste Debecker, John Martin, François Damanet

Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the spectral theory of dissipative phase transitions to non-Markovian systems, encompassing a much broader class of quantum materials and experiments and opening many possibilities for non-Markovian engineering of matter phases such as, as explored in the companion Letter [Debecker et al., Phys. Rev. Lett. 133, 140403 (2024)], reshaping of phase boundaries and triggering of phase transitions. We first prove several statements about the connections between the spectrum of the generator of the non-Markovian dynamics of general systems and dissipative phase transitions. Then, as a benchmark, we show that our framework can capture all the expected signatures of the superradiant phase transition appearing in a challenging $\mathbb{U}(1)$ -symmetric two-mode Dicke model from a reduced description of the dynamics of the atoms only, a task for which all other methods have failed so far.Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the spectral theory of dissipative phase transitions to non-Markovian systems, encompassing a much broader class of quantum materials and experiments and opening many possibilities for non-Markovian engineering of matter phases such as, as explored in the companion Letter [Debecker et al., Phys. Rev. Lett. 133, 140403 (2024)], reshaping of phase boundaries and triggering of phase transitions. We first prove several statements about the connections between the spectrum of the generator of the non-Markovian dynamics of general systems and dissipative phase transitions. Then, as a benchmark, we show that our framework can capture all the expected signatures of the superradiant phase transition appearing in a challenging $\mathbb{U}(1)$-symmetric two-mode Dicke model from a reduced description of the dynamics of the atoms only, a task for which all other methods have failed so far.

arXiv:2410.18990Physical Review AOct 3, 202410 citations

Harnessing non-Markovian quantum memory by environmental coupling

Zhong‐Xiao Man, Yun‐Jie Xia, Rosario Lo Franco

Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in the absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for the zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in the absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for the zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.

arXiv:1506.08293Physical Review AJul 13, 201593 citations

Role of non-Markovian dissipation in quantum phase transitions: Tricriticality, spin squeezing, and directional symmetry breaking

Baptiste Debecker, Lukas Pausch, Jonathan Louvet +3 more

Understanding how to control phase transitions in quantum systems is at the forefront of research for the development of new quantum materials and technologies.Here, we study how the coupling of a quantum system to a non-Markovian environment, i.e., an environment with a frequency-dependent spectral density inducing memory effects, can be used to generate and reshape phase transitions and squeezing in matter phases.Focusing on a Lipkin-Meshkov-Glick model, we demonstrate that non-Markovian dissipation can be leveraged to engineer tricriticality via the fusion of 2 nd -order and 1 st -order critical points.We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of directional spontaneous symmetry breaking (DSSB) as a general framework to understand this phenomenon.We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology.Finally, we propose an experimental implementation of our non-Markovian model in cavity QED.Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.Understanding how to control phase transitions in quantum systems is at the forefront of research for the development of new quantum materials and technologies.Here, we study how the coupling of a quantum system to a non-Markovian environment, i.e., an environment with a frequency-dependent spectral density inducing memory effects, can be used to generate and reshape phase transitions and squeezing in matter phases.Focusing on a Lipkin-Meshkov-Glick model, we demonstrate that non-Markovian dissipation can be leveraged to engineer tricriticality via the fusion of 2 nd -order and 1 st -order critical points.We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of directional spontaneous symmetry breaking (DSSB) as a general framework to understand this phenomenon.We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology.Finally, we propose an experimental implementation of our non-Markovian model in cavity QED.Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.

Physical Review AJun 24, 20254 citations

The role of non-Markovian dissipation in quantum phase transitions: tricriticality, spin squeezing, and directional symmetry breaking

Baptiste Debecker, Lukas Pausch, Jonathan Louvet +3 more

Understanding how to control phase transitions in quantum systems is at the forefront of research for the development of new quantum materials and technologies. Here, we study how the coupling of a quantum system to a non-Markovian environment, i.e., an environment with a frequency-dependent spectral density inducing memory effects, can be used to generate and reshape phase transitions and squeezing in matter phases. Focusing on a Lipkin-Meshkov-Glick model, we demonstrate that non-Markovian dissipation can be leveraged to engineer tricriticality via the fusion of $2^{\mathrm{nd}}$ -order and $1^{\mathrm{st}}$ -order critical points. We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of \textit{directional spontaneous symmetry breaking} (DSSB) as a general framework to understand this phenomenon. We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology. Finally, we propose an experimental implementation of our non-Markovian model in cavity QED. Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.Understanding how to control phase transitions in quantum systems is at the forefront of research for the development of new quantum materials and technologies. Here, we study how the coupling of a quantum system to a non-Markovian environment, i.e., an environment with a frequency-dependent spectral density inducing memory effects, can be used to generate and reshape phase transitions and squeezing in matter phases. Focusing on a Lipkin-Meshkov-Glick model, we demonstrate that non-Markovian dissipation can be leveraged to engineer tricriticality via the fusion of $2^{\mathrm{nd}}$-order and $1^{\mathrm{st}}$-order critical points. We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of \textit{directional spontaneous symmetry breaking} (DSSB) as a general framework to understand this phenomenon. We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology. Finally, we propose an experimental implementation of our non-Markovian model in cavity QED. Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.

arXiv:2504.11317Apr 15, 20250 citations

Non-Markovian dynamics and quantum information probes

Pinja Haikka

This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.

Jun 14, 20130 citations

\mathbb{U}(1)

-symmetric two-mode Dicke model from a reduced description of the dynamics of the atoms only, a task for which all other methods have failed so far.

2^{\mathrm{nd}}

-order and

1^{\mathrm{st}}

-order critical points. We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of \textit{directional spontaneous symmetry breaking} (DSSB) as a general framework to understand this phenomenon. We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology. Finally, we propose an experimental implementation of our non-Markovian model in cavity QED. Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.