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Measurement-enhanced determination of BEC phase diagrams

Mark G. Bason, Robert K. Heck, M. Napolitano, Ottó Elíasson, Romain Müller, Aske R. Thorsen, Wenzhuo Zhang, J. Arlt, Jacob Friis Sherson

Published Jul 11, 2016• 0 citations
OpenAlex

Abstract

We demonstrate how dispersive atom number measurements during evaporative cooling can be used for enhanced determination of the non-linear parameter dependence of the transition to a Bose-Einstein condensate (BEC). Our analysis demonstrates that conventional averaging of shot-to-shot fluctuations introduces systematic errors and reduces precision in comparison with our method. We furthermore compare in-situ images from dispersive probing of a BEC with corresponding absorption images in time-of-flight. This allows for the determination of the transition point in a single experimental realization by applying multiple dispersive measurements. Finally, we explore the continuous probing of several consecutive phase transition crossings using the periodic addition of a focused dimple potential.

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Measurement-enhanced determination of BEC phase transitions

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Abstract We demonstrate how dispersive atom number measurements during evaporative cooling can be used for enhanced determination of the parameter dependence of the transition to a Bose–Einstein condensate (BEC). In this way shot-to-shot fluctuations in initial conditions are detected and the information extracted per experimental realization is increased. We furthermore calibrate in situ images from dispersive probing of a BEC with corresponding absorption images in time-of-flight. This allows for the determination of the transition point in a single experimental realization by applying multiple dispersive measurements. Finally, we explore the continuous probing of several consecutive phase transition crossings using the periodic addition of a focused ‘dimple’ potential.

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Phase contrast imaging is used to observe Bose-Einstein condensates (BECs) at finite temperature in situ. The imaging technique is used to accurately derive the absolute phase shift of a probe laser beam due to both the condensate and the thermal cloud. The accuracy of the method is enhanced by using the periodicity of the intensity signal as a function of the accumulated phase. The measured density profiles can be described using a two relevant parameter fit, in which only the chemical potential and the temperature are to be determined. This allows us to directly compare the measured density profiles to different mean-field models in which the interaction between the condensed and thermal atoms is taken into account to various degrees.

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Dispersive measurement of spin shot noise in a Bose-Einstein condensate

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We report dispersive spin shot noise measurement of a Bose-Einstein condensate (BEC). While dispersive probing has been used for quantum spin noise measurement of thermal and cold gases for decades, confirmative measurement of shot noise of real spin, i.e., the linear dependence of the spin variance on the number of atoms in a BEC, has been lacking. Here, we demonstrate precise spin noise measurement of a BEC of rubidium atoms at the spin shot noise level by polarization rotation using a two-color probe at optimal detunings, with power balance stabilization to suppress probe-induced excess spin noise. This work opens the possibility for the unexplored study of quantum spin fluctuations in multicomponent or spinor BECs and offers an approach to improve spin measurement precision, which is relevant to atomic spin-based sensors.

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Bose-Einstein condensation (BEC) in dilute gases stands as a fascinating phenomenon of quantum mechanics. In this state, hundreds of thousands of atoms occupy the lowest energy level, establishing a collective macroscopic quantum state, with numerous intriguing properties. BEC has become a fundamental tool for the exploration of quantum physics and it may facilitate further advancements in quantum technology, for instance, in quantum simulation and sensing applications. Due to the potential of BECs in both basic research and technology, a fundamental understanding of this phenomenon is essential to guarantee the precision and reliability of its applications. Atom number fluctuations in BECs stand as an unresolved fundamental problem that has posed significant theoretical challenges for nearly eight decades. The experimental observation of this effect has recently become feasible. However, a direct comparison between theoretical predictions and experimental results remains outstanding. In particular, technical challenges persist in the accurate detection of the BEC, and a thorough understanding of estimation errors is lacking. This PhD thesis addresses some of these challenges in the field. Firstly, it introduces an enhanced calibration method for time-of-flight absorption images of ultracold atomic clouds, improving the accuracy of such measurements. Additionally, a thorough statistical analysis of uncertainties in the preparation and parameter estimation of partially condensed Bose gases is presented, leading to an improved understanding of atom number fluctuations in BEC. Finally, this thesis presents the experimental advances toward a new project within the research group: Electromagnetically induced transparency (EIT). EIT is a concept where an otherwise opaque cloud can be made transparent through manipulation of its quantum states. Notably, these advancements include the construction of setups for an optical dipole trap and a hybrid trap, along with the development of systems enabling precise control of magnetic fields. This laid the groundwork for recent demonstrations of EIT within the group.

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Summary form only given. We have systematically studied BECs of /sup 87/Rb atoms in the regime of phase-fluctuating condensates. We observe the phase fluctuations by measuring the density distribution of the released cloud after ballistic expansion. By varying the temperature, the number of atoms in the condensate and the aspect ratio of the trapping potential, we studied the continuous transition from the usual 3D regime, where phase fluctuations are low, into the regime of strong phase fluctuations in the condensate. To determine the amount of phase fluctuations experimentally, we measured the formation and structure of stripes in the atomic density distribution after ballistic expansion as a function of the above mentioned parameters. The appearance of stripes after switching off the trapping fields can be understood as conversion of phase fluctuations respect. phase gradients into axial velocity fields and consecutive density distributions. These results are in good agreement with theoretical and numerical studies and set clear limitations on applications of BECs e.g. in interferometric measurements.

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Physical Review A•May 27, 2010•71 citations
We demonstrate how dispersive atom number measurements during evaporative cooling can be used for enhanced determination of the non-linear parameter dependence of the transition to a Bose-Einstein condensate (BEC). Our analysis demonstrates that conventional averaging of shot-to-shot fluctuations introduces systematic errors and reduces precision in comparison with our method. We furthermore compare in-situ images from dispersive probing of a BEC with corresponding absorption images in time-of-flight. This allows for the determination of the transition point in a single experimental realization by applying multiple dispersive measurements. Finally, we explore the continuous probing of several consecutive phase transition crossings using the periodic addition of a focused dimple potential.
Abstract We demonstrate how dispersive atom number measurements during evaporative cooling can be used for enhanced determination of the parameter dependence of the transition to a Bose–Einstein condensate (BEC). In this way shot-to-shot fluctuations in initial conditions are detected and the information extracted per experimental realization is increased. We furthermore calibrate in situ images from dispersive probing of a BEC with corresponding absorption images in time-of-flight. This allows for the determination of the transition point in a single experimental realization by applying multiple dispersive measurements. Finally, we explore the continuous probing of several consecutive phase transition crossings using the periodic addition of a focused ‘dimple’ potential.
Phase contrast imaging is used to observe Bose-Einstein condensates (BECs) at finite temperature in situ. The imaging technique is used to accurately derive the absolute phase shift of a probe laser beam due to both the condensate and the thermal cloud. The accuracy of the method is enhanced by using the periodicity of the intensity signal as a function of the accumulated phase. The measured density profiles can be described using a two relevant parameter fit, in which only the chemical potential and the temperature are to be determined. This allows us to directly compare the measured density profiles to different mean-field models in which the interaction between the condensed and thermal atoms is taken into account to various degrees.
We report dispersive spin shot noise measurement of a Bose-Einstein condensate (BEC). While dispersive probing has been used for quantum spin noise measurement of thermal and cold gases for decades, confirmative measurement of shot noise of real spin, i.e., the linear dependence of the spin variance on the number of atoms in a BEC, has been lacking. Here, we demonstrate precise spin noise measurement of a BEC of rubidium atoms at the spin shot noise level by polarization rotation using a two-color probe at optimal detunings, with power balance stabilization to suppress probe-induced excess spin noise. This work opens the possibility for the unexplored study of quantum spin fluctuations in multicomponent or spinor BECs and offers an approach to improve spin measurement precision, which is relevant to atomic spin-based sensors.
Bose-Einstein condensation (BEC) in dilute gases stands as a fascinating phenomenon of quantum mechanics. In this state, hundreds of thousands of atoms occupy the lowest energy level, establishing a collective macroscopic quantum state, with numerous intriguing properties. BEC has become a fundamental tool for the exploration of quantum physics and it may facilitate further advancements in quantum technology, for instance, in quantum simulation and sensing applications. Due to the potential of BECs in both basic research and technology, a fundamental understanding of this phenomenon is essential to guarantee the precision and reliability of its applications. Atom number fluctuations in BECs stand as an unresolved fundamental problem that has posed significant theoretical challenges for nearly eight decades. The experimental observation of this effect has recently become feasible. However, a direct comparison between theoretical predictions and experimental results remains outstanding. In particular, technical challenges persist in the accurate detection of the BEC, and a thorough understanding of estimation errors is lacking. This PhD thesis addresses some of these challenges in the field. Firstly, it introduces an enhanced calibration method for time-of-flight absorption images of ultracold atomic clouds, improving the accuracy of such measurements. Additionally, a thorough statistical analysis of uncertainties in the preparation and parameter estimation of partially condensed Bose gases is presented, leading to an improved understanding of atom number fluctuations in BEC. Finally, this thesis presents the experimental advances toward a new project within the research group: Electromagnetically induced transparency (EIT). EIT is a concept where an otherwise opaque cloud can be made transparent through manipulation of its quantum states. Notably, these advancements include the construction of setups for an optical dipole trap and a hybrid trap, along with the development of systems enabling precise control of magnetic fields. This laid the groundwork for recent demonstrations of EIT within the group.
Summary form only given. We have systematically studied BECs of /sup 87/Rb atoms in the regime of phase-fluctuating condensates. We observe the phase fluctuations by measuring the density distribution of the released cloud after ballistic expansion. By varying the temperature, the number of atoms in the condensate and the aspect ratio of the trapping potential, we studied the continuous transition from the usual 3D regime, where phase fluctuations are low, into the regime of strong phase fluctuations in the condensate. To determine the amount of phase fluctuations experimentally, we measured the formation and structure of stripes in the atomic density distribution after ballistic expansion as a function of the above mentioned parameters. The appearance of stripes after switching off the trapping fields can be understood as conversion of phase fluctuations respect. phase gradients into axial velocity fields and consecutive density distributions. These results are in good agreement with theoretical and numerical studies and set clear limitations on applications of BECs e.g. in interferometric measurements.
Phase contrast imaging is used to observe Bose-Einstein condensates at finite temperature in situ. The imaging technique is used to accurately derive the absolute phase shift of a probe laser beam due to both the condensate and the thermal cloud. The accuracy of the method is enhanced by using the periodicity of the intensity signal as a function of the accumulated phase. The measured density profiles can be described using a two-relevant-parameter fit, in which only the chemical potential and the temperature are to be determined. This allows us to directly compare the measured density profiles to different mean-field models in which the interaction between the condensed and the thermal atoms is taken into account to various degrees.