Closed-System Solution of the 1D Atom from Collision Model

Abstract

Obtaining the total wavefunction evolution of interacting quantum systems provides access to important properties, such as entanglement, shedding light on fundamental aspects, e.g., quantum energetics and thermodynamics, and guiding towards possible application in the fields of quantum computation and communication. We consider a two-level atom (qubit) coupled to the continuum of travelling modes of a field confined in a one-dimensional chiral waveguide. Originally, we treated the light-matter ensemble as a closed, isolated system. We solve its dynamics using a collision model where individual temporal modes of the field locally interact with the qubit in a sequential fashion. This approach allows us to obtain the total wavefunction of the qubit-field system, at any time, when the field starts in a coherent or a single-photon state. Our method is general and can be applied to other initial field states.

Anomalous energy exchanges and Wigner-function negativities in a single-qubit gate

“…In this regime, the rotating-wave approximation is allowed [18], and the coupling g can be considered uniform in frequency [19]. The field's lowering operator at the position x in the interaction picture [15][16][17] is given by b…”

“…We study the 1D atom using a collision model [14], where individual temporal modes of the electromagnetic field locally interact with the qubit in a sequential fashion [15,16]. When the field is prepared in a resonant coherent state, this method provides the exact analytical expression of the qubit-field entangled state at any time [17]. From the collision model of the driven 1D atom, we derive the analytical expression of the field's Husimi-Q function conditioned on the outcomes of the final qubit's measurement.…”

Multipartite Correlations in Quantum Collision Models

“…On the other hand, quantum physicists find new applications of quantum collision models in simulations of open quantum many-body dynamics [29,30] (including simulations on noisy intermediate-scale quantum processors [31]), relaxation processes caused by the dilute gas environment [32], quantum thermodynamics [33], and quantum thermometry [34,35]. Collisional picture of repeated interactions also takes place in quantum optics and waveguide quantum electrodynamics, where the electromagnetic field is represented in the form of discrete time-bin modes interacting with a quantum emitter [36][37][38][39][40][41][42][43][44][45][46][47][48][49]; however, the time-bin modes constituting the radiation field can be correlated so that the system dynamics becomes non-Markovian and exhibits memory effects in general. Besides the initially correlated state of ancillary particles or modes [46][47][48][49][50][51], memory effects in quantum collision models appear also as a result of two-ancilla collisions in between the system-ancilla collisions, where the latest involved ancilla interacts with the one that would interact with the system during the next collision [52][53][54][55].…”

“…This scenario takes place, e.g., when the second system starts interacting with an array of ancillas that were originally uncorrelated but previously interacted with the first system in the standard collision model [65,66]. Alternatively, the ancillas can represent time-bin correlated modes in the structured electromagnetic radiaion [36][37][38][39][40][41][42][43][44][45][46][47][48][49] or particles in a correlated spin chain, e.g., spin-1 particles in the ground state of the Affleck-Kennedy-Lieb-Tesaki (AKLT) antiferromagnetic Hamiltonian [70]. Ref.…”

Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks

“…Collision models naturally emerge in time-bin quantum optics and waveguide quantum electrodynamics, where the radiation field is mapped into a stream of discrete time-bin modes of duration τ [30][31][32][33][34][35][36][37][38][39] that sequentially interact with the quantum system while the radiation field propagates in space, see Fig. 1(a).…”