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arXiv:cond-mat/0510634 · Physical Review Letters

Spin-3 Chromium Bose-Einstein Condensates

Luis Santos, Tilman Pfau

Published May 16, 2006• 190 citations
arXivHTMLPDF

Abstract

We analyze the physics of spin-3 Bose-Einstein condensates, and, in particular, the new physics expected in ongoing experiments with condensates of chromium atoms. We first discuss the ground-state properties, which, depending on still unknown chromium parameters, and for low magnetic fields, can present various types of phases. We also discuss the spinor dynamics in chromium spinor condensates, which present significant qualitative differences when compared to other spinor condensates. In particular, dipole-induced spin relaxation may lead for low magnetic fields to transfer of spin into angular momentum similar to the well-known Einstein-de Haas effect. Additionally, a rapid large transference of population between distant magnetic states also becomes possible.

DOI
10.1103/physrevlett.96.190404

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We analyze the physics of spin-3 Bose-Einstein condensates, and, in particular, the new physics expected in ongoing experiments with condensates of chromium atoms. We first discuss the ground-state properties, which, depending on still unknown chromium parameters, and for low magnetic fields, can present various types of phases. We also discuss the spinor dynamics in chromium spinor condensates, which present significant qualitative differences when compared to other spinor condensates. In particular, dipole-induced spin relaxation may lead for low magnetic fields to transfer of spin into angular momentum similar to the well-known Einstein-de Haas effect. Additionally, a rapid large transference of population between distant magnetic states also becomes possible.
Dipole-dipole interactions are long-ranged and anisotropic. They induce a coupling between spin and angular momentum degrees of freedom yielding new interesting physics in the field of dilute quantum gases. We have thoroughly studied dipolar relaxation DR processes in a chromium BEC transferred into an excited magnetic m = +3 sublevel and loaded in 1D and 2D optical lattices. We demonstrate and quantify how the confinement of a quantum gas in optical lattices deeply modifies the DR processes. In particular, we show that DR is strongly inhibited at low magnetic fields when the released energy becomes smaller than the vibrational quantum of energy at the bottom of the lattice wells. We show that interband transitions are induced above the corresponding threshold and that metastability of the "excited state BEC" is reached below the 2D threshold.
We study the thermal activation of spin fluctuations in dynamically stable spinor Bose-Einstein condensates. We analyze the specific cases of a nondipolar spin-1 condensate in the state m=0m=0m=0, where thermal activation results from spin-changing collisions, and of a chromium condensate in the maximally stretched state $m=\ensuremath{-}3$, where thermal spin fluctuations are due to dipole-induced spin relaxation. In both cases, we show that the low energy associated to the spinor physics may be employed for thermometry purposes down to extremely low temperatures, typically impossible to measure in Bose-Einstein condensates with the usual thermometric techniques. Moreover, the peculiar dependence of the system's entropy with the applied Zeeman energy opens a possible route for adiabatic cooling.
We numerically study the dynamics of a spinor chromium condensate in low magnetic fields. We show that the condensate evolution has a resonant character revealing a rich structure of resonances similar to that already discussed in the case of alkali-metal-atom condensates. This indicates that dipolar resonances occur commonly in systems of cold atoms. In fact, they have already been observed experimentally. We further simulate two recent experiments with chromium condensates in which the threshold in spin relaxation and spontaneous demagnetization phenomena were observed. We demonstrate that both these effects originate in the resonant dynamics of chromium condensates.
This tutorial presents a detailed discussion of the generation of a Bose–Einstein condensate (BEC) of chromium atoms. This constitutes the first realization of a Bose–Einstein condensate of atoms with strong dipole–dipole interaction. Due to the special electronic and magnetic properties of chromium atoms, standard methods cannot be applied to generate a chromium BEC. The tutorial contains a detailed discussion of the techniques that we use to create the chromium BEC. Compared to all other BECs that have been created so far, chromium atoms have an extraordinarily large magnetic dipole moment and therefore underlie strong magnetic dipole–dipole interaction which is in contrast to the contact interaction that stems from s-wave scattering of the atoms, long-range and anisotropic. A steadily growing number of theoretical publications show that many interesting new phenomena are expected to occur in a 'dipolar' BEC. An experimental investigation of the expansion dynamics of the chromium BEC provides the first experimental proof of a mechanical effect of dipole–dipole interaction in a gas. We describe the condensate by a hydrodynamic model of a superfluid that takes dipole–dipole interaction into account. Our experimental results are in excellent agreement with this theory. We are able to determine the relative strength parameter of the dipole–dipole interaction and deduce the s-wave scattering length of chromium atoms. These two quantities allow us to completely describe the interaction of the atoms in the condensate. The experimental results presented here make the chromium BEC the most promising system for further investigations of dipolar effects in degenerate quantum gases.
We have observed Bose-Einstein condensation of chromium atoms [1], whose large magnetic dipole moment is unique among all species that have been Bose-condensed so far. The arising magnetic forces are of anisotropic and long-range character and therefore introduce a novel type of interaction in the physics of ultracold quantum gases. In addition, it is expected that the character of the interaction present in a chromium BEC can be varied from mainly contact to purely dipolar utilizing one of the recently observed Feshbach resonances in 52Cr-collisions.
Magnetic dipole-dipole interactions (MDDIs) are long-ranged and anisotropic. They induce a coupling between spin and angular momentum degrees of freedom paving the way for new interesting physics in the fields of quantum gases and magnetism. This paper thoroughly studies dipolar relaxation (DR) processes in a chromium BEC. Atoms are transferred from the absolute ground state with m = -3 to the excited m = +3 Zeeman state and are loaded in a 3D optical lattice; the magnetic state distribution of this system under various conditions is monitored. In a previous publication, it was demonstrated how the confinement of a quantum gas in 1D and 2D optical lattices deeply modifies the DR processes. In particular, it was shown that DR is inhibited at low magnetic fields when the released energy becomes smaller than the vibrational quantum of energy at the bottom of the lattice wells. In the present work, instability (or decay) of the “excited state BEC” appears as a resonant process as the released energy matches band excitation. Analyzing these resonances as a function of the magnetic field orientation reveals a new manifestation of the anisotropy of MDDIs. The spectroscopy of these resonances as a function of the field intensity is found to be sensitive to the lattice site number occupancy as demonstrated by performing it after various system preparation schemes including number-squeezed Mott states. Decays from sites housing three atoms produce entangled spin and orbital states.