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Register a new userOrthogonality Catastrophe as a Consequence of the Quantum Speed Limit
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A remarkable feature of quantum many-body systems is the orthogonality catastrophe which describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system whose variance in ground state energy scales with the system size exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems -- the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.
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We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two distinct species is suddenly switched on (quenched). We examine the behavior of the densities, the entanglement, the Loschmidt echo and the spectral function for a large range of inter-species interactions and find that even in such small systems evidence of Andersons orthogonality catastrophe can be witnessed.
We monitor the correlated quench induced dynamical dressing of a spinor impurity repulsively interacting with a Bose-Einstein condensate. Inspecting the temporal evolution of the structure factor three distinct dynamical regions arise upon increasing the interspecies interaction. These regions are found to be related to the segregated nature of the impurity and to the ohmic character of the bath. It is shown that the impurity dynamics can be described by an effective potential that deforms from a harmonic to a double-well one when crossing the miscibility-immiscibility threshold. In particular, for miscible components the polaron formation is imprinted on the spectral response of the system. We further illustrate that for increasing interaction an orthogonality catastrophe occurs and the polaron picture breaks down. Then a dissipative motion of the impurity takes place leading to a transfer of energy to its environment. This process signals the presence of entanglement in the many-body system.
Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, on the other hand, have attracted a great deal of attention in the last few years. In this article, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a trade-off relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the steady state. Based on this, we define a figure of merit called bounding second order cooling rate and show that this scales linearly with the unitary interaction strength among the constituent qubits. We also study the increase of bounding second order cooling rate with the thermalization strength. We subsequently demonstrate that coherence in the initial three qubit system can significantly increase the bounding second order cooling rate. We study the efficiency of the refrigerator at maximum bounding second order cooling rate and, in a limiting case, we show that the efficiency at maximum bounding second order cooling rate is given by a simple formula reminiscent of the Curzon-Ahlborn relation.
Geometric quantum speed limits quantify the trade-off between the rate with which quantum states can change and the resources that are expended during the evolution. Counterdiabatic driving is a unique tool from shortcuts to adiabaticity to speed up quantum dynamics while completely suppressing nonequilibrium excitations. We show that the quantum speed limit for counterdiabatically driven systems undergoing quantum phase transitions fully encodes the Kibble-Zurek mechanism by correctly predicting the transition from adiabatic to impulse regimes. Our findings are demonstrated for three scenarios, namely the transverse field Ising, the Landau-Zener, and the Lipkin-Meshkov-Glick models.
We perform a comprehensive analysis of the set of parameters ${r_{i}}$ that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time $tau$, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between $tau$ and the energy spectrum and allowing the classification of ${r_{i}}$ into families organized in a 2-simplex, $delta^{2}$. Furthermore, the states determined by ${r_{i}}$ are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those $r_{i}$s in $delta^{2}$ correspondent to states whose orthogonality time is limited by the Mandelstam--Tamm bound from those restricted by the Margolus--Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.
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