Disertación sobre el gas Tonks-Girardeau - descripción teórica y experimental

We investigate transition of a one-dimensional interacting Bose gas from a strongly repulsive regime to a strongly attractive regime, where a stable highly excited state known as the super Tonks-Girardeau gas was experimentally realized very recently. By solving exact dynamics of the integrable Lieb-Liniger Bose gas, we demonstrate that such an excited gas state can be a very stable dynamic state. Furthermore we calculate the breathing mode of the super Tonks-Girardeau gas which is found to be in good agreement with experimental observation. Our results show that the highly excited super Tonks-Girardeau gas phase can be well understood from the fundamental theory of the solvable Bose gas.We investigate transition of a one-dimensional interacting Bose gas from a strongly repulsive regime to a strongly attractive regime, where a stable highly excited state known as the super Tonks-Girardeau gas was experimentally realized very recently. By solving exact dynamics of the integrable Lieb-Liniger Bose gas, we demonstrate that such an excited gas state can be a very stable dynamic state. Furthermore we calculate the breathing mode of the super Tonks-Girardeau gas which is found to be in good agreement with experimental observation. Our results show that the highly excited super Tonks-Girardeau gas phase can be well understood from the fundamental theory of the solvable Bose gas.

arXiv:0911.1936Physical Review AMar 25, 201057 citations

Das Verfolgen einer Idee: Plancks Theorie idealer Gase

Dieter Hoffmann, Massimiliano Badino

Springer eBooksJan 1, 20100 citations

Metafísica experimental y mecánica cuántica

Luis de la Peña, Ana María Cetto K.

Ciencias (México, D.F.)Jan 1, 20020 citations

Two super-Tonks-Girardeau states of a trapped one-dimensional spinor Fermi gas

Marvin D. Girardeau

A harmonically trapped ultracold 1D spinor Fermi gas with a strongly attractive 1D even-wave interaction induced by a 3D Feshbach resonance is studied. It is shown that it has two different super Tonks-Girardeau (sTG) energy eigenstates which are metastable against collapse in spite of the strong attraction, due to their close connection with 1D hard sphere Bose gases which are highly excited gaslike states. One of these sTG states is a hybrid between an sTG gas with strong $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ attractions and an ideal Fermi gas with no $(\ensuremath{\uparrow}\ensuremath{\uparrow})$ or $(\ensuremath{\downarrow}\ensuremath{\downarrow})$ interactions, the sTG component being an exact analog of the recently observed sTG state of a 1D ultracold Bose gas. It should be possible to create it experimentally by a sudden switch of the $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ interaction from strongly repulsive to strongly attractive, as in the recent Innsbruck experiment on the bosonic sTG gas. The other is a trapped analog of a recently predicted sTG state which is an ultracold gas of strongly bound $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ fermion dimers which behave as bosons with a strongly attractive boson-boson interaction leading to sTG behavior. It is proved that the probability of a transition from the ground state for strongly repulsive interaction to this dimer state under a sudden switch from strongly repulsive to strongly attractive interaction is $\ensuremath{\ll}$ $1$ , contrary to a previous suggestion.A harmonically trapped ultracold 1D spinor Fermi gas with a strongly attractive 1D even-wave interaction induced by a 3D Feshbach resonance is studied. It is shown that it has two different super Tonks-Girardeau (sTG) energy eigenstates which are metastable against collapse in spite of the strong attraction, due to their close connection with 1D hard sphere Bose gases which are highly excited gaslike states. One of these sTG states is a hybrid between an sTG gas with strong $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ attractions and an ideal Fermi gas with no $(\ensuremath{\uparrow}\ensuremath{\uparrow})$ or $(\ensuremath{\downarrow}\ensuremath{\downarrow})$ interactions, the sTG component being an exact analog of the recently observed sTG state of a 1D ultracold Bose gas. It should be possible to create it experimentally by a sudden switch of the $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ interaction from strongly repulsive to strongly attractive, as in the recent Innsbruck experiment on the bosonic sTG gas. The other is a trapped analog of a recently predicted sTG state which is an ultracold gas of strongly bound $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ fermion dimers which behave as bosons with a strongly attractive boson-boson interaction leading to sTG behavior. It is proved that the probability of a transition from the ground state for strongly repulsive interaction to this dimer state under a sudden switch from strongly repulsive to strongly attractive interaction is $\ensuremath{\ll}$$1$, contrary to a previous suggestion.

arXiv:1004.2925Physical Review AJul 20, 201063 citations

Wave functions of the super-Tonks-Girardeau gas and the trapped one-dimensional hard-sphere Bose gas

Marvin D. Girardeau, G. E. Astrakharchik

Recent theoretical and experimental results demonstrate a close connection between the super-Tonks-Girardeau (STG) gas and a one-dimensional (1D) hard-sphere Bose (HSB) gas with hard-sphere diameter nearly equal to the 1D scattering length ${a}_{1\mathrm{D}}$ of the STG gas, a highly excited gaslike state with nodes only at interparticle separations $|{x}_{j\ensuremath{\ell}}|={x}_{\mathrm{node}}\ensuremath{\approx}{a}_{1\mathrm{D}}$. It is shown herein that when the coupling constant ${g}_{B}$ in the Lieb-Liniger interaction ${g}_{B}\ensuremath{\delta}({x}_{j\ensuremath{\ell}})$ is negative and $|{x}_{12}|\ensuremath{\geqslant}{x}_{\mathrm{node}}$, the STG and HSB wave functions for $N=2$ particles are not merely similar, but identical; the only difference between the STG and HSB wave functions is that the STG wave function allows a small penetration into the region $|{x}_{12}|<{x}_{\mathrm{node}}$ , whereas for a HSB gas with hard-sphere diameter ${a}_{\mathrm{hs}}={x}_{\mathrm{node}}$ , the HSB wave function vanishes when $|{x}_{12}|<{a}_{\mathrm{hs}}$ . Arguments are given suggesting that the same theorem holds also for $N>2$ . The STG and HSB wave functions for $N=2$ are given exactly in terms of a parabolic cylinder function, and for $N\ensuremath{\geqslant}2$, ${x}_{\mathrm{node}}$ is given accurately by a simple parabola. The metastability of the STG phase generated by a sudden change of the coupling constant from large positive to large negative values is explained in terms of the very small overlap between the ground state of the Tonks-Girardeau gas and collapsed cluster states.Recent theoretical and experimental results demonstrate a close connection between the super-Tonks-Girardeau (STG) gas and a one-dimensional (1D) hard-sphere Bose (HSB) gas with hard-sphere diameter nearly equal to the 1D scattering length ${a}_{1\mathrm{D}}$ of the STG gas, a highly excited gaslike state with nodes only at interparticle separations $|{x}_{j\ensuremath{\ell}}|={x}_{\mathrm{node}}\ensuremath{\approx}{a}_{1\mathrm{D}}$. It is shown herein that when the coupling constant ${g}_{B}$ in the Lieb-Liniger interaction ${g}_{B}\ensuremath{\delta}({x}_{j\ensuremath{\ell}})$ is negative and $|{x}_{12}|\ensuremath{\geqslant}{x}_{\mathrm{node}}$, the STG and HSB wave functions for $N=2$ particles are not merely similar, but identical; the only difference between the STG and HSB wave functions is that the STG wave function allows a small penetration into the region $|{x}_{12}|<{x}_{\mathrm{node}}$, whereas for a HSB gas with hard-sphere diameter ${a}_{\mathrm{hs}}={x}_{\mathrm{node}}$, the HSB wave function vanishes when $|{x}_{12}|<{a}_{\mathrm{hs}}$. Arguments are given suggesting that the same theorem holds also for $N>2$. The STG and HSB wave functions for $N=2$ are given exactly in terms of a parabolic cylinder function, and for $N\ensuremath{\geqslant}2$, ${x}_{\mathrm{node}}$ is given accurately by a simple parabola. The metastability of the STG phase generated by a sudden change of the coupling constant from large positive to large negative values is explained in terms of the very small overlap between the ground state of the Tonks-Girardeau gas and collapsed cluster states.

arXiv:0912.1633Physical Review AJun 21, 201035 citations

Une théorie de la relativité expérimentale

Anthony Piermattéo

Jan 1, 20250 citations

1

, contrary to a previous suggestion.

{a}_{1\mathrm{D}}

of the STG gas, a highly excited gaslike state with nodes only at interparticle separations $|{x}_{j\ensuremath{\ell}}|={x}_{\mathrm{node}}\ensuremath{\approx}{a}_{1\mathrm{D}}$. It is shown herein that when the coupling constant

{g}_{B}

in the Lieb-Liniger interaction ${g}_{B}\ensuremath{\delta}({x}_{j\ensuremath{\ell}})$ is negative and $|{x}_{12}|\ensuremath{\geqslant}{x}_{\mathrm{node}}$, the STG and HSB wave functions for

N=2

particles are not merely similar, but identical; the only difference between the STG and HSB wave functions is that the STG wave function allows a small penetration into the region

|{x}_{12}|<{x}_{\mathrm{node}}

, whereas for a HSB gas with hard-sphere diameter

{a}_{\mathrm{hs}}={x}_{\mathrm{node}}

, the HSB wave function vanishes when

|{x}_{12}|<{a}_{\mathrm{hs}}

. Arguments are given suggesting that the same theorem holds also for

N>2

. The STG and HSB wave functions for

N=2

are given exactly in terms of a parabolic cylinder function, and for $N\ensuremath{\geqslant}2$,

{x}_{\mathrm{node}}

is given accurately by a simple parabola. The metastability of the STG phase generated by a sudden change of the coupling constant from large positive to large negative values is explained in terms of the very small overlap between the ground state of the Tonks-Girardeau gas and collapsed cluster states.