Questions tagged [cold-atoms]
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102
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Quasi-classical energies for neutron in gravitational potential [closed]
Lets consider a ultra cold neutron gas in a gravitational potential. The known quasi-classical energy up to the classical turning point is
$$
E_n =\sqrt[3]{\frac{9m}{8}(\pi\hbar g (n-\frac{1}{4}))^2} ...
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1
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Energy conservation in Kapitza-Dirac diffraction?
In Kapitza-Dirac diffraction, a standing wave of light (wavevector of single wave $k$) is pulsed on for a very short period of time ($\sim \mu s$) onto a bunch of cold atoms. This results in the atoms ...
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Polarization of light and transitions in a Magneto Optical Trap
After reading this question, I realized that I didn't really understand how a MOT works in detail. I was always relying on the simplistic picture given in textbooks which never addresses the actual ...
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When are two fermions considered identical?
I am a bit confused about the terminology concerning identical fermions. In quantum mechanics, identical fermions need to obey certain anticommutation relations i.e. have an antisymmetric total ...
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Looking for chemicals to melt ice
This might sound like science fiction but I am trying to learn if there is a chemical or material that can convert cold into heat. It also could be kinetic as well. An example would be placing a ...
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2
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What is the advantage of making a BEC in space?
The NASA Cold Atom Laboratory, which I believe is slated to launch this year, has the goal of putting a Bose Einstein Condensate (BEC) apparatus on the ISS. What is the advantage of doing this? ...
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Is Bose-Einstein condensate in the optical lattice a single mode condensate?
I recently read about BEC loaded into the optical lattice p.200
Looking at a condensate released from a lattice after a
time of flight typically on the order of a few milliseconds
amounts to ...
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Optical pumping & spin-changing collisions
Optical pumping is the method of 'pumping' all the electrons in the upmost $m_F$ state of the ground state, by shining $\sigma^+$ light such that eventually all the electrons end up in this state ...
- 23.9k
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364
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Arbitrariness of phase in the definition of the Fock state leads to lack of squeezing
Every state in quantum mechanics is defined up to a global phase. In other words, quantum states $|\psi'\rangle = e^{i\varphi}|\psi\rangle$ which differ just by a phase factor are indistinguishable. ...
- 2,030
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Labelling hyperfine structure states in strong magnetic field
I am trying to work out the frequency shifts to the hyperfine energy levels in $^{39}$K $\,$ S$_{1/2}$ (the ground state).
I diagonalise the Hamiltonian for different values of the $B_z$ field, with ...
- 23.9k
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2
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Dipole interaction for a two-level system in a trap potential
Consider a two-level system under the following Hamiltonian:
$H=H_{I}+H_{E}+H_{dip}$
where $H_I$ is the Hamiltonian for the two internal states of the two-level system $span \{\left |e \right> {,}...
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Is 3D optical lattice just a stack of 2D lattices?
I am confused about the idea of 3D optical lattice. Many papers use 3D optical lattice to study bosons behavior, but is it really a 3D system where atoms interact in all three directions or is it just ...
- 2,030
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The calculation of the entropy of a single atom
I used to think that the entropy of a single atom could not be calculated, for in my mind only the entropy of a system containing many atoms could be calculated.
But my professor told me the entropy ...
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Can a naked eye see a single atom when it is resonantly driven by some laser beam? [duplicate]
Presumably, when the laser is strong enough, the fluorescence will be very strong too. So, is it possible to see a single atom with a naked eye?
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How does Sisyphus cooling work in a photon picture?
Some years ago, during my masters degree, I took a short course on cold matter, which included a component on laser cooling and trapping taught by Ed Hinds. On the lecture on Sisyphus cooling, he ...
- 127k
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Thomas-Fermi approximation for cold atoms in a 1D harmonic potential
The Time-independent Gross-Pitaevskii equation is
$$
\mu{\phi(x)}=\Big(\frac{-\hbar^{2}}{2m}\nabla^{2}+V_{ext}(x)+g|\phi(x)|^{2}\Big)\phi(x)
$$
From Thomas-Fermi approximation,
$$
\phi(x)=\sqrt{\...
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Natural linewidth of hyperfine levels?
The D2 line of $^{87}\mathrm{Rb}$ is the transition between the $5^2\mathrm P_{3/2}$ and the $5^2\mathrm S_{1/2}$ states. Its linewidth $\Gamma$ is always quoted to be $\sim 6\ \mathrm{MHz}$.
But both ...
- 23.9k
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Frequency modulation in laser locking - what frequency?
In laser locking, e.g. using the PDH technique, the light (say of frequency $f$) is modulated so as to add two symmetric sidebands of frequency $\Omega$.
I know the maths, I understand how this leads ...
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Why the total nuclear spin is only 0 or 2 for singlet s-wave scatting with $M_F=0$?
when I read the lecture of Feshbach resonance, the lecture on page 15 said that it want to find all s-wave molecules for $M_F=0$. It said when the two atoms are singlet, the total nuclear spin is only ...
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How to perform stroboscopic measurements for Floquet topological insulators?
Floquet topological insulators (arXiv:1008.1792, arXiv:1211.5623) have attracted much research interests in condensed matter physics. The goal is to realize topological insulators from trivial ...
- 11.3k
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Can we 'dope' a fluid to make it become a superfluid?
The only element that can become a superfluid is Helium (He-3 and He-4) since it does not solidify not matter how cold it gets, hence it can reach the superfluid transition temperature whilst still a ...
- 23.9k
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$U(1)$ gauge symmetry in superfluid
The conventional superfluid phase in a Bose-Hubbard ground state has $U(1)$ symmetry. In the presence of spin-orbit coupling (SOC), the superfluid ground state has non-uniform phases. Why do people in ...
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How is it possible to combine various techniques in cold atom experiments?
I’ve been reading about laser-trapped cold atoms (6Li in particular, which is a fermion) and was amazed at the number of things to keep track of in the experiments, just to gain that degree of control ...
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Interactions and scattering length in Feshbach resonances
In the context of cold atoms, one can make use of the Feshbach resonance mechanism to alter the sign and value of the two-particle scattering length by applying and varying an external magnetic field. ...
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Ground state symmetry breaking in Bose-Hubbard model with spin-orbit coupling
The Hamiltonian for 2D Bose-Hubbard model with spin-orbit coupling on a square lattice is written as
$
H = -t\sum_{\langle ij \rangle}\Psi_i^{\dagger}\Psi_j^{\vphantom{\dagger}}
+ \frac{U}{2}\sum_{i\...
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Why isn't ice a good electrical conductor?
Water can conduct electricity, and some solids can conduct. Why can't ice? Are ice molecules too packed together to let valence shell electrons bounce across each other to create electrical charge? ...
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Can one make a synthetic dimension "curl around" into a cylinder?
A really cool recent proposal,
Synthetic Gauge Fields in Synthetic Dimensions. A. Celi et al. Phys. Rev. Lett. 112, 043001 (2014), arXiv:1307.8349,
shows how you can simulate a synthetic magnetic ...
- 127k
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Why is the atom loss rate enhanced at the Feshbach resonance?
At the Feshbach resonance, the scattering length is enhanced. But why is the atom loss also enhanced?
- 1,139
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coherent states phase-space topology
Quantum mechanics can be formulated in various different ways. One of these is the so called phase space formulation, where we use quasi-probability distribution functions. The most recognized is the ...
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Proof of Kohn's theorem
In 1961 W. Kohn's paper ( Phys. Rev. 123, 1242 (1961) ) first stated that the electron-electron interaction does not change the cyclotron resonance frequency in a bulk three dimensional gas.
I can ...
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When would the Gross-Pitaevskii equation break down as $a\rightarrow \infty$?
It is now common to use Feshbach resonance to tune the s-wave scattering length of a Bose-Einstein condensate.
Apparently as $a\rightarrow \infty$, the GPE would break down. The reason is that it ...
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compressibility of cold atoms in optical lattices
The compressibility of cold bosons in an optical lattice is defined as $\kappa = \frac{\partial \langle n\rangle}{\partial \mu}$, where $\langle n\rangle$ is the density and $\mu$ is the chemical ...
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Superfluid-Mott insulator transition in Bose-Hubbard model in terms of vortex condensation
I have heard that there is some effective field theoretic type understanding of the superfluid-Mott insulator transition in Bose-Hubbard model. It says if the system is in a superfluid phase where the ...
- 1,516
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Effective Potential of experienced by a particle with contact interaction in an optical lattice
Suppose i have an optical lattice with particles loaded onto it, the potential due to the optical lattice is $V_{0}Cos\left(x\right)$. Assume that the particles interact with eachother through contact ...
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How to distinguish Bose glass and superfluid phases in a harmonic trap?
In mean-field study of Bose-Hubbard model in an optical lattice, what parameter can be calculated to distinguish Bose glass and superfluid in a harmonic trap?
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Thomas-Fermin approximation of cold atoms in a harmonic trap
In Bose-Hubbard model of cold atoms, one can use Thomas-Fermi approximation to get a rough number of total particle number. In Thomas-Fermi approximation, the site density is $n(R_i)=（\mu-\kappa R_i^2）...
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Why the trap is needed in cold atom experiment?
In ultracold atomic gas experiments, the optical lattice provides a periodic optical potential to trap the atoms, why an extra trap, usually a harmonic trap is needed to trap the atoms?
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How to load Bose-Einstein Condensates into an optical lattice?
In cold atom experiments, what techniques are used to load Bose-Einstein Condensates into an optical lattice??
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596
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Gutzwiller mean-field method in Bose Hubbard model
Gutzwiller mean-felid method is an efficient way to study Bose-Hubabrd model in optical lattice with a harmonic trap. Gutzwiller method assumes there is no spatial correlation within the trap, so ...
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Experimental Measurement of Quantum phase transition in an optical lattice
In Greiner and coauthors' seminal paper, the cold atoms are confined in a harmonic trap. So different many-body phases may coexist in the trap at a given lattice depth. For a deep lattice, there will ...
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What is the difference between atomic limit and hard core boson limit?
In Bose-Hubbard model, we neglect the hopping term in atomic limit (U>>t) and the dominant interaction term result in a Mott Insulator phase. In hard core boson limit ($U \rightarrow \infty$), there ...
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Nomenclature clarification concerning solitons
My experience with solitons is restricted to the classical setting, namely solutions to the quartic interaction $\phi^4$, the Sine-Gordon equation, and Korteweg–de Vries equations. I was explicit to ...
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Are the recently observed Dirac monopoles separable?
I just went through Observation of Dirac monopoles in a synthetic magnetic field.
What exactly has been observed?
More importantly, are these monopoles localized inside the apparatus (no stray ...
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Coupling of open and closed channels in Feshbach resonance model
Feshbach resonance is described with coupling of 2 systems differing in the form of potentials :- one is said to produce a bound state (in 'closed' channel) and other is to produce scattering states (...
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What is a degenerate Fermi gas?
In ultracold atoms, it is generally talked of a degenerate Fermi gas. What does degenerate mean here?
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Quantum Quench Problem
I read about the quantum quench problem in condensed matter physics.
But what does really mean? Has anybody a good explanation about the origin of quantum quench problem?
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How to realize long-range interaction of colds atom in an optical lattice?
In the Bose-Hubbard model of cold atoms in an optical lattice, we consider only the short-range interaction or on-site interaction. Is it possible to realize long-range interaction similar to Coulomb ...
- 2,399
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Correct way to do a Thomas-Fermi approximation for cold gases
I have calculated the total Gross-Pitaevskii energy for a 2D Bose-Einstein condensate in an harmonical trap, using a variational gaussian wave function with a variational parameter b. Now I want to ...
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0
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Single-site superfluid wave function and coherent state
The Superfluid wavefunction in Bose Hubbard model can be written as $|\Psi_{SF}\rangle=\frac{1}{\sqrt{N!}}(b_{k=0}^{\dagger})^N|0\rangle$ in the U=0 limit, whereU is the onsite interaction, N is the ...
- 2,399
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relative phase/sign in $\Psi$ after exchange of composite particles with angular momenta
I'm reading Quantum Liquids by A.J. Leggett and became confused by the following statement in the first chapter.
Consider now a pair of such identical atoms. In the absence of appreciable coupling ...
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