Quantum Brownian Motion in Bose-Einstein Condensates Submitted in partial fulfillment of the requirements of the degree of Doctor of Philosophy by Christos Charalambous Supervisor Prof. M. Lewenstein Co-Supervisor Dr. M.-A. Garcia-March UNIVERSITAT POLITECNICA DE CATALUNYA (2020) Dedicated to ”FAMILY” Acknowledgments ”...I hope for nothing, I fear for nothing, I am free...” N. Kazantzakis This PhD thesis is the result of my ”Brownian motion” in life, starting from Cyprus, moving through London, Zurich and finally Barcelona, where certain forces that pushed me towards my current state appear to be less random than others and worth explicit mentioning. I first thank my supervisor Maciej Lewenstein for giving me the opportunity to undertake this PhD in his group, allowing me to pursue the research directions that I found interesting. I also thank my cosupervisor Miguel-Angel Garcia-March for support- ing me in the difficult moments of my PhD and encouraging me in my first steps as a researcher. Without doubt, important contributions to the completion of this thesis had Aniello Lampo, Gorka Mu˜noz-Gil, Mohammad Mehboudi and Arnau Riera. ◗✇❝ ❛♠❢✐❜♦❧❛ ♠✇❝✱ ♦♥❛❝ ①❡❦✐♥➔❡✐ ♥❛ ❞✐❞❛❦♦✐❦ st❛ ✷✼ ♠♦✉✱ ➔♠♦✉♥❛ ➔❞❤ ♠✐❛ ❦❛❧❼ ❞✐❛♠♦❢✇♠♥❤ ♣♦✇♣✐❦❤❛ ❦❛✐ ✇❝ ❡❦ t♦♦✉ ❥❡✇➳ ì✐ ♥❛ ♠❡❣❼❧♦ ♠♦❝ t✇♥ ❡✉❛✐s✐✲ ➳♥ ♠♦✉ ♣♣❡✐ ♥❛ ❛♣♦❞♦❥❡ s❡ ì❧❡❝ ❡❦❡♥❡❝ ✐❝ ✧❞✉♥❼♠❡✐❝✢ ♣♦✉ ✉♥❜❛❧❛♥ st♦♥ ❤♠❛✐♠ ❤❝ ♣♦✇♣✐❦❤❛❝ ♣♦✉ ❡♠❛✐ ➔♠❡❛✱ ♣✐♥ ①❡❦✐♥➔✇ ✐❝ ❞✐❞❛❦♦✐❦❝ ♠♦✉ ♣♦✉❞❝✳ ❍❧♦✉ ❢❛❡✐♥❡♦ ❡♥❛✐ ì✐ ♣➳♦✐ ❤♥ ❧st❛ ♠❡ ❛✉♦❝ t♦✉❝ ♦♣♦♦✉❝ ♦❢❡❧✇ ♥❛ ❡✉❛✐s➔✇ ❜❦♦♥❛✐ ♦✐ ❣♦♥❡❝ ♠♦✉✳ ❆♥❛♠❢❜♦❧❛✱ ❤ ✉♥❡✐❢♦❼ t♦✉❝ ❤♥ ③✇➔ ♠♦✉ ♠♣♦❡ ♠♥♦ ♥❛ ❛❛❦❤✐❥❡ ❡✇❝ ❛♥ ❤♥ st❛❥❡➔❝ ❦❛❡❥✉♥❤❝ ❛✉♦❢✉➔❝ ❞♥❛♠❤ ♣♦✉ ✉♥❛♥❼ ❦❛♥❡❝ ❤♥ ❦♥❤❤ t✇♥ ✧❡♥❡❣➳♥ ✇♠❛✐❞✇♥ t♦✉ ▼♣❼♦✉♥✧✳ ❖ ♣❛❛❧❧❤❧✐♠❝ ❛✉❝ ❥❡✇➳ ì✐ ❡♥❛✐ ❛❦✐❜➔❝ ♠✐❛❝ ❦❛✐ ①✇ ì✐ ♣❼♥t❛ ♥❛ ❦♦♠♠❼✐ t♦✉ ❡❛✉♦ ♠♦✉ ❥❛ ❦❛❥♦❞❤❣❡t❛✐ st❛❥❡❼ ❛♣ ✐❝ ❛①❡❝ ❦❛✐ t♦ ➔❥♦❝ ♣♦✉ ♠♦✉ ♦✉♥ ❡♠❢✉➔❡✐ ❦❛✐ ❣✐❛ t❛ ♦♣♦❛ ❥❛ t♦✉❝ ❡♠❛✐ ❛✐➳♥✐❛ ❡✉❣♥➳♠✇♥✳ ▼❤❛ ❛❛ ❛❝ ❛❣❛♣➳ ❦❛✐ ❛❝ ❡✉❛✐st➳ ❡❦ ❜❼❥♦✉❝ ❦❛❞❛❝✳ ◗✇❝ ❡❼❝ ♣♦t❛ ❛♣ ❛ ✇ ❦❛❛❢❡✐ ❞❡♥ ❥❛ ➔❛♥ ❡❢✐❦✳ ❖❢❡❧✇ ❡♣❤❝ ♥❛ ❡✉❛✐s➔✇ ì❧❛ t❛ ❼♦♠❛ ♣♦✉ ♠❡ t♦♥ ♥❛ ➔ t♦♥ ❼❧❧♦ ♣♦ ♣Ðs❡②❛♥ ❡ ❡♠♥❛✱ ❦❛✐ ♠❡ t♦♥ ♣♦ t♦✉❝ ♦ ❦❛❥♥❛❝✱ ♠♦✉ ❞✇❛♥ ❤♥ ❛♣❛❛❤❤ ❛✉♦♣❡♣♦❥❤❤ ❣✐❛ ♥❛ ♣❡✇ ì✐ ✇ ♣❡❡✐ ♠✐ ➔♠❡❛✳ ❙❡ ❛✉➔ ❤♥ ❦❛❤❣♦❛ ♣❡✐❧❛♠❜❼♥♦♥❛✐ ♣♦❢❛♥➳❝ ì❧❛ t❛ ❼♦♠❛ ❤❝ ♦✐❦♦❣♥❡✐❛❝ ♠♦✉ ❤♥ ❑♣♦✱ ♣♦✉ ♠❡ t♦♥ ♦ ♦✐❦♦❣♥❡✐❛ ❞❡♥ ❛♥❛❢♦♠❛✐ ♠♥♦ st❛ ❼♦♠❛ ♣♦✉ ✉♥❞♦♠❛✐ ❡① ❛♠❛♦❝✳ ❊✉❛✐st➳ ì❧♦✉❝ t♦✉❝ ❛♥❥➳♣♦✉❝ ♣♦✉ ❣♥➳✐❛ st♦ ▲♦♥❞♥♦✱ ❤♥ ❩✉rÐ❤ ❦❛✐ ❤♥ ❇❛❦❡❧➳♥❤ ❦❛✐ t♦✉❝ ♦♣♦♦✉❝ ♠♣♦➳ ♥❛ ❛♣♦❦❛❧➳ ♣❛❣♠❛✐❦♦❝ ❢❧♦✉❝✳ ♦❢❛♥➳❝ ❛✉♦ ♣♦✉ ❥❛ t♦ ❞✐❛❜❼♦✉♥ ①♦✉♥ ❡ ♣♦✐♦❝ ❛♥❛❢♦♠❛✐✳ ❚❧♦❝ ♣♣❡✐ ♥❛ ❡✉❛✐s➔✇ ❤♥ ❦♦♣❧❛ ♠♦✉ ▲❼♦✉❛ ♣♦✉ ❡ ❛✉ì t♦ ❡❧❡✉❛♦ èt♦❝ t♦✉ ❞✐❞❛❦♦✐❦♦ ♠♦✉ ✉♣➔①❡ ♥❛ ❛❢❛❧❝ ❧✐♠❼♥✐ ♣♦✉ ♣❼♥❛ ➔①❡❛ ì✐ ♠♣♦♦❛ ♥❛ ❛♥✐♠❡✇♣s✇ ✐❝ ❢♦✉♦♥❡❝ ♣♦✉ ♦♥❛♥✳ ❙❛❝ ❡✉❛✲ ✐st➳ ì❧♦✉❝ ♦✉❝ ✉♥❡✐❢❛❡ ♠❡ t♦♥ ♥❛ ➔ t♦♥ ❼❧❧♦ ♣♦ st♦ ♥❛ ❡✐ ❤ ▼♣❛♦✉♥✐❛♥➔ ♠♦✉ ❦♥❤❤ ♠✐❛ t♦ ♠♦❢❤ ❦❛❡❥✉♥❤ ❡❧✐❦❼✦ C. Charalambous LIST OF PUBLICATIONS Journal Papers included in this Thesis 1. C. Charalambous, M. A. Garc´ıa-March, G. Munoz-Gil, P. R. Grzybowski and M. Lewenstein, (2019), Control of anomalous diffusion of a Bose polaron in a coherently coupled two-component BEC, arxiv:1910.01571 (Submitted to Quantum). 2. C. Charalambous, M. A. Garc´ıa-March, M. Mehboudi and M. Lewenstein, (2019), Heat current control in trapped BEC, New J. of Physics, 21 (8), 083037. 3. M. Mehboudi, A. Lampo, C. Charalambous, L. A. Correa, M. A. Garc´ıa-March and M. Lewenstein,(2019), Using polarons for sub-nk quantum non-demolition thermom- etry in a Bose-Einstein condensate, Phys. Rev. Lett. 122 (3), 030403. 4. C. Charalambous, M. A. Garc´ıa-March, A. Lampo, M. Mehboudi and M. Lewen- stein, (2019), Two distinguishable impurities in BEC: squeezing and entanglement of two Bose polarons, SciPost 6 (10). Other Journal Papers 5. A. Lampo, C. Charalambous, M. A. Garc´ıa-March and M. Lewenstein, (2018),Non- Markovian polaron dynamics in a trapped Bose-Einstein condensate, Phys. Rev. A 98 (6), 063630. 6. T. R. de Oliveira, C. Charalambous, D. Jonathan, M. Lewenstein and A. Riera, (2018), Equilibration time-scales in closed many-body quantum systems, New J. of Physics 20 (3), 033032. 7. G. Mu˜noz-Gil, C. Charalambous, M. A. Garc´ıa-March, M. F. Garcia-Parajo, C. Manzo, M. Lewenstein and A. Celi, (2017), Transient subdiffusion from an Ising environment, Phys. Rev. E 96, 052140. 8. C. Charalambous, G. Mu˜noz-Gil, A. Celi, M. F. Garcia-Parajo, M. Lewenstein, C. Manzo, and M. A. Garc´ıa-March, (2017), Nonergodic subdiffusion from transient interactions with heterogeneous partners, Phys. Rev. E 95, 032403 . ii Abstract English version Quantum Brownian motion is one of the most prominent examples of an open quantum system, a system which cannot be treated in isolation, due to the unavoidable interaction with the surrounding environment. There are a number of methods to study the dynam- ics of a system undergoing such a type of motion, and recently it was shown that the simplest one that satisfies Heisenberg Uncertainty principle is the approach of Quantum Generalized Langevin Equations (QGLE). This is also the method used throughout this thesis. A Quantum Brownian motion approach was used to study a plethora of systems, among them the Bose polaron problem. In this case, one transforms the original prob- lem into one where the impurities are treated as quantum Brownian particles interacting with a bath composed of the Bogoliubov modes of the condensate. Then by deriving the relevant QGLE, it was shown that the dynamics of the Bose polaron exhibit memory effects. This was studied for both a free BEC and a harmonically trapped one. Taking advantage of this recent theoretical development, we study a number of phenomena that can be examined under this prism and show how various microdevices can be constructed and controlled. In the first project, we study the creation of entanglement and squeezing of two uncou- pled impurities that are immersed in a single common Bose-Einstein condensate (BEC) bath. We treat these impurities as two quantum Brownian particles as explained above. We study two scenarios:(i) In the absence of an external potential, we observe sudden death of entanglement;(ii) In the presence of an external harmonic potential, where en- tanglement survives even at the asymptotic time limit. In our study we consider experi- mentally tunable parameters. In our second work, we studied the diffusive behavior of a Bose Polaron immersed in a coherently coupled two-component BEC. The particle superdiffuses if it couples in the same manner to both components, i.e. if it couples either attractively or repulsively to both of them. This is the same behavior of an impurity immersed in a single BEC. Conversely, we find that it exhibits a transient nontrivial subdiffusive behavior if it couples attractively to one of the components and repulsively with the other. We show how the magnitude of the anomalous exponent reached and the duration of the subdiffusive interval can be controlled with the Rabi frequency of the coherent coupling between the two components and the coupling strength of the impurity to the BEC. Then we proceeded with the construction of two microdevices, a quantum sub-nk thermometer and a heat diode. In the first project, we introduced a novel minimally disturbing method for sub-nK thermometry in a Bose-Einstein condensate (BEC). Our technique again was based on the Bose polaron model where an impurity embedded in the BEC acts as the thermometer. We propose to detect temperature fluctuations from mea- surements of the position and momentum of the impurity. Crucially, these cause minimal backaction on the BEC and hence, realize a nondemolition temperature measurement. Following the paradigm of the emerging field of quantum thermometry, we combine tools from quantum parameter estimation and the theory of open quantum systems to solve the problem in full generality. We thus avoid any simplification, such as demanding thermalization of the impurity atoms, or imposing weak dissipative interactions with the BEC. Our method is illustrated with realistic experimental parameters common in many labs, thus showing that it can compete with state-of-the-art destructive techniques, even when the estimates are built from the outcomes of accessible (suboptimal) quadrature measurements. In our final work, we investigated the heat transport and the control of heat current among two spatially separated trapped Bose–Einstein Condensates (BECs), each of them at a different temperature. To allow for heat transport among the two independent BECs we consider a link made of two harmonically trapped impurities, each of them interacting with one of the BECs. Since the impurities are spatially separated, we consider long- range interactions between them, namely a dipole–dipole coupling. We study this system under theoretically suitable and experimentally feasible assumptions/parameters. The dynamics of these impurities is treated within the framework of the quantum Brownian motion model as before. We address the dependence of heat current and current–current correlations on the physical parameters of the system. Interestingly, we show that heat rectification, i.e. the unidirectional flow of heat, can occur in our system, when a periodic driving on the trapping frequencies of the impurities is considered. Therefore, our system is a possible setup for the implementation of a phononic circuit. Motivated by recent developments on the usage of BECs as platforms for quantum information processing, our work offers an alternative possibility to use this versatile setting for information transfer and processing, within the context of phononics, and more generally in quantum thermodynamics. Spanish version El movimiento Browniano,