Symmetries and Invariants for Non-Hermitian Hamiltonians

We discuss Hamiltonian symmetries and invariants for quantum systems driven by non-Hermitian Hamiltonians. For time-independent Hermitian Hamiltonians, a unitary or antiunitary transformation AHA that leaves the Hamiltonian H unchanged represents a symmetry of the Hamiltonian, which implies the commutativity [H, A] = 0 and, if A is linear and time-independent, a conservation law, namely the invariance of expectation values of A. For non-Hermitian Hamiltonians, H comes into play as a distinct operator that complements H in generalized unitarity relations. The above description of symmetries has to be extended to include also A-pseudohermiticity relations of the form AH = H A. A superoperator formulation of Hamiltonian symmetries is provided and exemplified for Hamiltonians of a particle moving in one-dimension considering the set of A operators that form Klein's 4-group: parity, time-reversal, parity&time-reversal, and unity. The link between symmetry and conservation laws is discussed and shown to be richer and subtler for non-Hermitian than for Hermitian Hamiltonians.This research was funded by Basque Country Government (grant number IT986-16), MINECO/FEDER, UE (grant number FIS2015-67161-P). M.A. Simon acknowledges support by the Basque Government predoctoral program (grant number PRE-2017-2-0051)

Noise Sensitivities for an Atom Shuttled by a Moving Optical Lattice via Shortcuts to Adiabaticity

We find the noise sensitivities (i.e., the quadratic terms of the energy with respect to the perturbation of the noise) of a particle shuttled by an optical lattice that moves according to a shortcut-to-adiabaticity transport protocol. Noises affecting different optical lattice parameters, trap depth, position, and lattice periodicity, are considered. We find generic expressions of the sensitivities for arbitrary noise spectra but focus on the white-noise limit as a basic reference, and on Ornstein–Uhlenbeck noise to account for the effect of non-zero correlation times.This work was supported by the Basque Country Government (Grant No. IT986-16), by PGC2018-101355- B-I00 (MCIU/AEI/FEDER,UE), and by the Key Research Project in Universities of Henan Province (Grant No. 20B140016

Claude Cohen-Tannoudji profesorea Zientzia eta Teknologia Fakultatean

1936. urtean sortu eta handik hilabete gutxira Gerra Zibilagatik itxi zen lehenbiziko euskal unibertsitate publikoa: Euzko Irakastola Nagusia zuen izena, eta unibertsitate hartako medikuntzako euskara (sendakintz-euzkera) irakasten zuen Jose Zinkunegi medikuaz, haren obraz eta haren euskaraz dihardu lan honek. Gaur egungo Euskal Herriko Unibertsitatea eta Euskara Teknikoa irakasgaia 1936ko unibertsitate haren eta irakasgai haren oinordeko dira, hurrenez hurren, eta haiei eta Iñaki Ugarteburu Gastañares zenari egin nahi diegun omenaldi gisa ulertu behar da hitzaldi hau

Fast Driving of a Particle in Two Dimensions without Final Excitation

Controlling the motional state of a particle in a multidimensional space is key for fundamental science and quantum technologies. Applying a recently found two-dimensional invariant combined with linear invariants, we propose protocols to drive a particle in two dimensions so that the final harmonic trap is translated and rotated with respect to the initial one. These protocols realize a one-to-one mapping between initial and final eigenstates at some predetermined time and avoid any final excitations.This work was supported by the National Natural Science Foundation of China (Grant No. 12104390), the Natural Science Foundation of Henan Province (Grant No. 212300410238), by Grant PID2021-126273NB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, by the Basque Government through Grant No. IT1470-22, and by the Scientific Research Innovation Team of Xuchang University (Grant No. 2022CXTD005)

Bi oszilagailu harmonikodun eredu minimalista baten bidezko bero-errektifikazioa

We study heat rectification using a minimalistic model of two different atoms trapped in harmonic potentials, where the atoms are subjected to effective Lan-gevin baths created by the Doppler cooling, while they interact by linear forces. We obtain analytical expressions for the steady state. If the exchange of baths is done changing temperature and friction coefficients at the same time an asymmetry of heat current is found. We also search for the highest asymmetry in the parameter space of the system.; Bero-errektifikazioa aztertzen dugu harrapatutako bi atomo ezberdi-nez osatutako modelo minimalista baten bidez. Atomoek indar linealak jasaten dituzte laserren bidez sorturiko Langevin bainu efektiboekin kontaktuan, Doppler efektuaren bidez sortuak. Egoera egonkorreko korronteen adierazpen analitikoak lortzen ditugu. Sistema lineal honetan bero-korronte asimetrikoa lortzen da bainuen tenperatura eta bainuek sistemarekiko duten akoplamendua aldi berean trukatzen badira. Modelo honen parametro- espazioa ere aztertzen dugu bero-korronte asimetria maximizatzeko