Quantum dynamics of Bose-polaron in a dd-dimensional Bose Einstein condensate

We study the quantum motion of an impurity atom immersed in a Bose Einstein condensate in arbitrary dimension. The Bogoliubov excitations of the Bose Einstein condensate act as a bosonic bath for the impurity. We present a detailed derivation of the $d$-dimensional Langevin equations that describe the quantum dynamics of the system, and of the associated generalized tensor that describes the spectral density in the full generality. When the impurity is not trapped, we calculate the mean square displacement, showing that the motion is super diffusive. We obtain also explicit expressions for the super diffusive coefficient in the small and large temperature limits. We find that, in the latter case, the maximal value of this coefficient is the same in all dimensions. We study also the behaviour of the average energy and compare the results for various dimensions. In the trapped case, we study squeezing and find that the stronger position squeezing can be obtained in lower dimensions. We quantify the non-Markovianity of the particle's motion, and find that it increases with dimensionality.Comment: 18 pages, 12 figure

Engineering single-phonon number states of a mechanical oscillator via photon subtraction

We introduce an optomechanical scheme for the probabilistic preparation of single-phonon Fock states of mechanical modes based on photo-subtraction. The quality of the produced mechanical state is confirmed by a number of indicators, including phonon statistics and conditional fidelity. We assess the detrimental effect of parameters such as the temperature of the mechanical system and address the feasibility of the scheme with state-of-the-art technology.Comment: 7 pages, 10 figures, RevTeX4; This paper supersedes arXiv:1511.07617; Accepted for publication in Phys. Rev.

Quantum dynamics of Bose-polaron in a d-dimensional Bose Einstein condensate

We study the quantum motion of an impurity atom immersed in a Bose Einstein condensate in arbitrary dimension. The Bogoliubov excitations of the Bose Einstein condensate act as a bosonic bath for the impurity. We present a detailed derivation of the d-dimensional Langevin equations that describe the quantum dynamics of the system, and of the associated generalized tensor that describes the spectral density in the full generality. When the impurity is not trapped, we calculate the mean square displacement, showing that the motion is super diffusive. We obtain also explicit expressions for the super diffusive coefficient in the small and large temperature limits. We find that, in the latter case, the maximal value of this coefficient is the same in all dimensions. We study also the behaviour of the average energy and compare the results for various dimensions. In the trapped case, we study squeezing and find that the stronger position squeezing can be obtained in lower dimensions. We quantify the non-Markovianity of the particle's motion, and find that it increases with dimensionality.We thank A. Lampo for encouraging and motivating discussions. M.M.K. and H.T. acknowledge support from Fundação para a Ciência e a Tecnologia (FCT-Portugal) through Grant No. PD/BD/114345/2016 and through Contract No. IF/00433/2015 respectively. H.T. and J.T.M. acknowledge the financial support from the Quantum Flagship Grant PhoQuS (Grant No. 820392) of the European Union. M.A.G.-M. acknowledges funding from the Spanish Ministry of Education and Vocational Training (MEFP) through the Beatriz Galindo program 2018 (BEAGAL18/00203). ICFO group acknowledges support from ERC AdG NOQIA, Spanish Ministry of Economy and Competitiveness (“Severo Ochoa” program for Centres of Excellence in R&D (CEX2019-000910-S), Plan National FIDEUA PID2019-106901GB-I00/10.13039/501100011033, FPI), Fundació Privada Cellex, Fundació Mir-Puig, and from Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341, CERCA program, QuantumCAT _U16-011424, co-funded by ERDF Operational Program of Catalonia 2014-2020), MINECO-EU QUANTERA MAQS (funded by State Research Agency (AEI) PCI2019-111828-2/10.13039/501100011033), EU Horizon 2020 FET-OPEN OPTOLogic (Grant No 899794), and the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314. J.W. was partially supported by the U.S. National Science Foundation grant DMS 1615045. C.C. acknowledges support from María de Maeztu Program for Centers and Units of Excellence in R&D (MDM-2017-0711).With funding from the Spanish government through the "Severo Ochoa Centre of Excellence" accreditation (CEX2019-000910-S).N