arXiv:1607.04897 · Physical Review A

Isothermal compressibility determination across Bose-Einstein condensation

Freddy Jackson Poveda-Cuevas, P. C. M. Castilho, E. D. Mercado-Gutiérrez, A. R. Fritsch, Sérgio Ricardo Muniz, E. Lucioni, G. Roati, Vanderlei Salvador Bagnato

Published Jul 31, 2015• 16 citations

arXiv HTML PDF

Abstract

We apply the global thermodynamic variables approach to experimentally determine the isothermal compressibility parameter ${\ensuremath{\kappa}}_{T}$ of a trapped Bose gas across the phase transition. We demonstrate the behavior of ${\ensuremath{\kappa}}_{T}$ around the critical pressure, revealing the second-order nature of the phase transition. Compressibility is the most important susceptibility to characterize the system. The use of global variables shows advantages with respect to the usual local density approximation method and can be applied to a broad range of situations.

DOI: 10.1103/physreva.92.013638

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arXiv:1607.04897 · Physical Review A

Isothermal compressibility determination across Bose-Einstein condensation

Freddy Jackson Poveda-Cuevas, P. C. M. Castilho, E. D. Mercado-Gutiérrez, A. R. Fritsch, Sérgio Ricardo Muniz, E. Lucioni, G. Roati, Vanderlei Salvador Bagnato

Published Jul 31, 2015• 16 citations

arXiv HTML PDF

Abstract

We apply the global thermodynamic variables approach to experimentally determine the isothermal compressibility parameter

{\ensuremath{\kappa}}_{T}

of a trapped Bose gas across the phase transition. We demonstrate the behavior of

{\ensuremath{\kappa}}_{T}

around the critical pressure, revealing the second-order nature of the phase transition. Compressibility is the most important susceptibility to characterize the system. The use of global variables shows advantages with respect to the usual local density approximation method and can be applied to a broad range of situations.

DOI: 10.1103/physreva.92.013638

Related papers

Coeficiente de expansão térmica de um gás de Bose durante a sua transição de fase

E. D. Mercado-Gutiérrez

Ultra cold quantum gas is a convenient system to study fundamental questions of modern physics, such as phase transitions and critical phenomena. This master thesis is devoted to experimental investigation of the thermodynamics susceptibilities, such as the isothermal compressibility and the thermal expansion coefficient of a trapped Bose-Einstein condensate (BEC) of 87Rb atoms. The critical phenomena and the critical exponents across the transition can explain the behavior of the isothermal compressibility and the thermal expansion coefficient near the critical temperature TC. By employing the developed formalism of global thermodynamics variables, we carry out a statistical treatment of Bose gas in a 3D harmonic potential. After that, comparison of obtained results reveals the most appropriate state variables describing the system, namely volume and pressure parameter V and Π respectively. The both are related with the confining frequencies and BEC density distribution. We apply this approach to define the set of new thermodynamic variables of BEC, and also to construct the isobaric phase diagram V T. Its allows us to extract the compressibility κT and the thermal expansion coefficient βΠ. The behavior of the isothermal compressibility corresponds to the second-order phase transition, while the thermal expansion coefficient around the critical point behaves as β ∼ tr-α, where tr is reduced temperature of the system and α is the critical exponent on the basic of these. Results we have obtained the critical exponent α = 0.15±0.09, which allows us to determine the system dimensionality by means of the scaling theory, relating the critical exponents with the dimensionality. As a result, we found out that the dimensionality of the system to be d ∼ 3, one is in agreement with the real dimension of the system.Ultra cold quantum gas is a convenient system to study fundamental questions of modern physics, such as phase transitions and critical phenomena. This master thesis is devoted to experimental investigation of the thermodynamics susceptibilities, such as the isothermal compressibility and the thermal expansion coefficient of a trapped Bose-Einstein condensate (BEC) of 87Rb atoms. The critical phenomena and the critical exponents across the transition can explain the behavior of the isothermal compressibility and the thermal expansion coefficient near the critical temperature TC. By employing the developed formalism of global thermodynamics variables, we carry out a statistical treatment of Bose gas in a 3D harmonic potential. After that, comparison of obtained results reveals the most appropriate state variables describing the system, namely volume and pressure parameter V and Π respectively. The both are related with the confining frequencies and BEC density distribution. We apply this approach to define the set of new thermodynamic variables of BEC, and also to construct the isobaric phase diagram V T. Its allows us to extract the compressibility κT and the thermal expansion coefficient βΠ. The behavior of the isothermal compressibility corresponds to the second-order phase transition, while the thermal expansion coefficient around the critical point behaves as β ∼ tr-α, where tr is reduced temperature of the system and α is the critical exponent on the basic of these. Results we have obtained the critical exponent α = 0.15±0.09, which allows us to determine the system dimensionality by means of the scaling theory, relating the critical exponents with the dimensionality. As a result, we found out that the dimensionality of the system to be d ∼ 3, one is in agreement with the real dimension of the system.

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BEC phase diagram of a $^{87}$ Rb trapped gas in terms of macroscopic thermodynamic parametersBEC phase diagram of a $^{87}$Rb trapped gas in terms of macroscopic thermodynamic parameters

Vı́ctor Romero-Rochı́n, R. F. Shiozaki, M. A. Caracanhas +4 more

We measure the phase diagram of a $^{87}$ Rb Bose gas in a harmonic trap in terms of macroscopic parameters obtained from the spatial distribution of atoms. Considering the relevant variables as size of the cloud ${\cal V}$ , number of atoms $N$ and temperature $T$ , a novel parameter $Π= Π(N,{\cal V},T)$ is introduced to characterize the overall pressure of the system. We construct the phase diagram ( $Π$ vs $T$ ) identifying new features related to Bose-Einstein condensation (BEC) transition in a trapped gas. A thermodynamic description of the phase transition based on purely macroscopic parameters, provide us with properties that do not need the local density approximation. An unexpected consequence of this analysis is the suggestion that BEC appears as a continuous third-order phase transition instead of being a second-order one.We measure the phase diagram of a $^{87}$Rb Bose gas in a harmonic trap in terms of macroscopic parameters obtained from the spatial distribution of atoms. Considering the relevant variables as size of the cloud ${\cal V}$, number of atoms $N$ and temperature $T$, a novel parameter $Π= Π(N,{\cal V},T)$ is introduced to characterize the overall pressure of the system. We construct the phase diagram ($Π$ vs $T$) identifying new features related to Bose-Einstein condensation (BEC) transition in a trapped gas. A thermodynamic description of the phase transition based on purely macroscopic parameters, provide us with properties that do not need the local density approximation. An unexpected consequence of this analysis is the suggestion that BEC appears as a continuous third-order phase transition instead of being a second-order one.

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Using a multiple-image reconstruction method applied to a harmonically trapped Bose gas, we determine the equation of state of uniform matter across the critical transition point, within the local density approximation. Our experimental results provide the canonical description of pressure as a function of the specific volume, emphasizing the dramatic deviations from the ideal Bose gas behavior caused by interactions. They also provide clear evidence for the nonmonotonic behavior with temperature of the chemical potential, which is a consequence of superfluidity and Bose-Einstein condensation. The measured thermodynamic quantities are compared to mean-field predictions available for the interacting Bose gas. The limits of applicability of the local density approximation near the critical point are also discussed, focusing on the behavior of the isothermal compressibility.Using a multiple-image reconstruction method applied to a harmonically trapped Bose gas, we determine the equation of state of uniform matter across the critical transition point, within the local density approximation. Our experimental results provide the canonical description of pressure as a function of the specific volume, emphasizing the dramatic deviations from the ideal Bose gas behavior caused by interactions. They also provide clear evidence for the nonmonotonic behavior with temperature of the chemical potential, which is a consequence of superfluidity and Bose-Einstein condensation. The measured thermodynamic quantities are compared to mean-field predictions available for the interacting Bose gas. The limits of applicability of the local density approximation near the critical point are also discussed, focusing on the behavior of the isothermal compressibility.

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A. R. Fritsch, P. E. S. Tavares, Franklin J. Vivanco +3 more

We present an alternative approach for determining the sound modes in atomic Bose-Einstein condensates, based on thermodynamic global variables. The total number of trapped atoms was carefully studied as a function of temperature across the phase transition, at constant volume. It allowed us to evaluate the first and second sound independently resulting in consistent values from the quantum to classical regime, in good agreement with previous results found in the literature. We also provide some insight on the dominant mode, either thermal or superfluid, on each sound velocity depending on the temperature rangeWe present an alternative approach for determining the sound modes in atomic Bose-Einstein condensates, based on thermodynamic global variables. The total number of trapped atoms was carefully studied as a function of temperature across the phase transition, at constant volume. It allowed us to evaluate the first and second sound independently resulting in consistent values from the quantum to classical regime, in good agreement with previous results found in the literature. We also provide some insight on the dominant mode, either thermal or superfluid, on each sound velocity depending on the temperature range

Jun 21, 20161 citation

We apply the global thermodynamic variables approach to experimentally determine the isothermal compressibility parameter

{\ensuremath{\kappa}}_{T}

of a trapped Bose gas across the phase transition. We demonstrate the behavior of

{\ensuremath{\kappa}}_{T}

{}^{87}

Rb Bose gas in a harmonic trap in terms of those macroscopic parameters obtained from the spatial distribution of atoms. Considering the relevant variables such as the trap potential $\mathcal{V}={({\ensuremath{\omega}}_{x}{\ensuremath{\omega}}_{y}{\ensuremath{\omega}}_{z})}^{\ensuremath{-}1}$, number of atoms

N

, and temperature

T

, a parameter $\ensuremath{\Pi}=\ensuremath{\Pi}(N,\mathcal{V},T)$ is introduced to characterize the overall macroscopic pressure of the system. We construct the phase diagram ($\ensuremath{\Pi}$ vs

T

) identifying the main features related to the Bose-Einstein condensation (BEC) transition in a trapped gas. A thermodynamic description of the phase transition based on purely macroscopic parameters provides us with a description that does not need the local-density approximation. This procedure can be used to explore different aspects related to BEC such as the nature of the phase transition in a trapped gas.

BEC phase diagram of a

^{87}

Rb trapped gas in terms of macroscopic thermodynamic parameters

We measure the phase diagram of a

^{87}

Rb Bose gas in a harmonic trap in terms of macroscopic parameters obtained from the spatial distribution of atoms. Considering the relevant variables as size of the cloud

{\cal V}

, number of atoms

N

and temperature

T

, a novel parameter

Π= Π(N,{\cal V},T)

is introduced to characterize the overall pressure of the system. We construct the phase diagram (

Π

T

) identifying new features related to Bose-Einstein condensation (BEC) transition in a trapped gas. A thermodynamic description of the phase transition based on purely macroscopic parameters, provide us with properties that do not need the local density approximation. An unexpected consequence of this analysis is the suggestion that BEC appears as a continuous third-order phase transition instead of being a second-order one.