arXiv subjects

Karol Gietka

Publications and source records attributed to Karol Gietka.

25 records · Page 2Linked to original sources

arXiv2021

Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model

We show how the dynamics of the Dicke model after a quench from the ground-state configuration of the normal phase into the superradiant phase can be described for a limited time by a simple inverted harmonic oscillator model and that this limited time approaches infinity in the thermodynamic limit. Although we specifically discuss the Dicke model, the presented mechanism can be also used to describe dynamical quantum phase transitions in other systems and opens a new avenue in simulations of physical phenomena associated with an inverted harmonic oscillator.

quant-ph↗

arXiv2021

Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.

quant-ph↗

arXiv2021

Cavity-enhanced magnetometer with a spinor Bose-Einstein condensate

We propose a novel type of composite light-matter magnetometer based on a transversely driven multi-component Bose-Einstein condensate coupled to two distinct electromagnetic modes of a linear cavity. Above the critical pump strength, the change of the population imbalance of the condensate caused by an external magnetic field entails the change of relative photon number of the two cavity modes. Monitoring the cavity output fields thus allows for nondestructive measurement of the magnetic field in real time. We show that the sensitivity of the proposed magnetometer exhibits Heisenberg-like scaling with respect to the atom number. For state-of-the-art experimental parameters, we calculate the lower bound on the sensitivity of such a magnetometer to be of the order of fT/$\sqrt{\mathrm{Hz}}$--pT/$\sqrt{\mathrm{Hz}}$ for a condensate of $10^4$ atoms with coherence times of the order of several ms.

quant-ph↗

arXiv2021

Simulating the same physics with two distinct Hamiltonians

We develop a framework and give an example for situations where two distinct Hamiltonians living in the same Hilbert space can be used to simulate the same physics. As an example of an analog simulation, we first discuss how one can simulate an infinite-range-interaction one-axis twisting Hamiltonian using a short-range nearest-neighbor-interaction Heisenberg XXX model with a staggered field. Based on this, we show how one can build an alternative version of a digital quantum simulator. As a by-product, we present a method for creating many-body maximally entangled states using only short-range nearest-neighbor interactions.

quant-ph↗

arXiv2019

A supersolid-based gravimeter in a ring cavity

We propose a novel type of composite light-matter interferometer based on a supersolid-like phase of a driven Bose-Einstein condensate coupled to a pair of degenerate counterpropagating electromagnetic modes of an optical ring cavity. The supersolid-like condensate under the influence of the gravity drags the cavity optical potential with itself, thereby changing the relative phase of the two {cavity electromagnetic fields}. Monitoring the phase evolution of the cavity output fields thus allows for a nondestructive measurement of the gravitational acceleration. We show that the sensitivity of the proposed gravimeter exhibits Heisenberg-like scaling with respect to the atom number. As the relative phase of the cavity fields is insensitive to photon losses, the gravimeter is robust against these deleterious effects. For state-of-the-art experimental parameters, the relative sensitivity $Δg/g$ of such a gravimeter could be of the order of $10^{-10}$--$10^{-8}$ for a condensate of a half a million atoms and interrogation time of the order of a few seconds.

quant-ph↗

arXiv2018

Multipartite-Entanglement Dynamics in Regular-to-Ergodic Transition: a Quantum-Fisher-Information approach

The characterization of entanglement is a central problem for the study of quantum many-body dynamics. Here, we propose the quantum Fisher information as a useful tool for the study of multipartite-entanglement dynamics in many-body systems. We illustrate this by considering the regular-to-ergodic transition in the Dicke model---a fully-connected spin model showing quantum thermalization above a critical interaction strength. We show that the QFI has a rich dynamical behavior which drastically changes across the transition. In particular, the asymptotic value of the QFI, as well as its characteristic timescales, witness the transition both through their dependence on the interaction strength and through the scaling with the system size. Since the QFI also sets the ultimate bound for the precision of parameter estimation, it provides a metrological perspective on the characterization of entanglement dynamics in many-body systems. Here we show that quantum ergodic dynamics allows for a much faster production of metrologically useful states.

cond-mat.stat-mech↗

arXiv2014

Simple atom interferometer in a double-well potential

We present a detailed study of an atom interferometer which can be realized in a double-well potential. We assume that the interferometric phase is imprinted in the presence of coherent tunneling between the wells. We calculate the ultimate bounds for the estimation sensitivity and show how they relate to the precision of the Mach-Zehnder interferometer. The interferometer presented here allows for sub shot-noise sensitivity when fed with the spin-squeezed states with reduced either the relative population imbalance or the relative phase. We also calculate the precision of the estimation from the population imbalance and show that it overcomes the shot-noise level when the entangled squeezed-states are used at the input.

cond-mat.quant-gas↗