Questions tagged [cold-atoms]
The cold-atoms tag has no usage guidance.
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What happens to the scattering cross section of two fermions with different spins at low temperature?
The scattering cross section for two identical fermions at low temperature is given by: $\sim 8\pi a_1^2(ka_1)^4$. I was wondering what happens if the two fermions have different spins - does it ...
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Does the size, and distance between, expanding ultracold gas clouds depend on the populations in each cloud?
Say you had some $^{87}Rb$ atoms at a few kelvin and you knew that the atoms were
distributed among the magnetic sub-levels of a hyperfine manifold. You want to know the relative population of each by ...
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Landau level in particular cases
If we consider an array of identical uncoupled spinless non-interacting one-dimensional wires, as shown in Fig.(a) with a single-particle electronic dispersion E(k), which we can take to be parabolic ...
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1answer
92 views
Why is the density of a BEC so low?
I've just begun reading C. Pethick and H. Smith's textbook "Bose-Einstein condensation in dilute gases" (Cam. Uni. Press). In the Introduction, they contrast the density of atoms at the centre of a ...
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How are atoms formes by electromagnetic waves that a specific frequency? [closed]
I came up something like this- Every piece of matter has a resonancefrequency or series of frequenciesbecause all matter is made up of atoms. Atoms are formed by electromagnetic waves that have a ...
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1answer
55 views
Is it BEC-BCS crossover the natural framework to explain superconductivity from ultracold atoms?
I know that superfluidity and superconductivity have very distinct characteristics and have specific theories. However, it seems that in ultra-cold atomic gases these phenomena can be understood by a ...
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1answer
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speed of freezing vs. moving [closed]
An idea came to my mind and like to discuss it.
We know that out there in the space the absolute zero (aka. -273 C) is almost reached where all the particles and atoms would freeze up and stop giving ...
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1answer
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In AMO experiments, how do cold alkali metal atoms remain gaseous?
My focus is on condensed matter physics, so I've never really explored this question although it always seemed curious to me. My "immediate reaction" intuition would dictate that cold metal atoms ...
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1answer
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What laser frequency is needed for the Doppler cooling of iron?
What laser frequency is needed for Doppler cooling iron? How do you determine this frequency?
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Is the ground state a Schrödinger cat state?
Consider the following Bose-Hubbard Hamiltonian which describes a Bose-Einstein condensate confined in a two-well potential:
$$
H= -T(a_L^\dagger a_R + a_L a_R^\dagger ) + \frac{U}{2}(n_L^2+n_R^2-...
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1answer
19 views
Fermi-Hubbard model: adiabatically change tunnelling
Consider the 3D Fermi-Hubbard model in a cold-atom setting (harmonic confinement, $\epsilon_i$):
$ H = - t \sum_{\langle i, j\rangle, \sigma} c^{\dagger}_{i, \sigma}c_{j,\sigma} + U\sum_{i}n_{i,\...
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1answer
100 views
What is the (quantum) definition of thermal equilibrium?
What is the necessary condition for a quantum system to be in thermal equilibrium? The quantum systems I have in mind are a bunch of cold atoms, of photons in a cavity.
Does a system need to obey a ...
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66 views
If an atom is in its ground state, has the atom the lower energy possible and there is its lower temperature?
"In the lowest energy state, the constituents of the atom (the nucleus and the orbiting electrons) are arranged so that the total energy in the system is minimal. This is called the ground state of ...
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1answer
88 views
Is there an intuitive reason as to why there is no phase transition to get to a degenerate Fermi gas?
Cooling a bosonic gas leads to a phase transition into the Bose-Einstein condesate. This is characterised by a symmetry broken ( U(1), by choosing a specific phase for the macroscopic wavefunction) ...
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Why does $[H,N]=0$ violate with superfluid phase judgement $\left<b\right>=0?$
I'm working with the standard Boson Hubbard model. It's Hamiltonian is defined in Fock space and commutes with total particle number N.
$$[{{\hat H}_{BH}},\hat N] = 0$$
So I can simultaneously ...
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1answer
50 views
Resource request: Superfluid helium
I am wondering if anybody could recommend any good textbooks on the subject. So far, I have discovered (but not yet had a chance to read), a chapter in Landau-Lifshitz fluid mechanics (love Landau-...
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1answer
153 views
Hard-core bosons and fermions - spinless?
The introduction to this paper about bosonic atoms expanding in an optical lattice says the following:
Are hard-core bosons mapped to spinless fermions?
Because this link shows the mapping ...
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Cold atoms: how does evaporative cooling work?
I understand the principle of evaporative cooling (for the creation of a Bose-Einstein Condensate), but I do not find any reference which explains mathematically this process and which explains what ...
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1answer
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Potential lineshapes of a BEC in a magnetic trap
We considere a Bose-Einstein Condensate (BEC) of atoms occupying a magneticaly trapped atomic state $|m_{F}=-1\rangle$. One can then use a radio-frequency field to extract atoms from the BEC by ...
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Feshbach resonance - Magnetic Field/Spin Orientation
I have been reading about Feshbach resonance in ultra cold atoms and there were some areas I'd like to understand better/have questions about:
i) As the atoms approach each other, can their spins be ...
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1answer
85 views
$\Delta \ell = 0, \ell = 0 \rightarrow \ell = 0$ transition in atomic ground state
Assume I am in the $S_{1/2}$ state of, say, Rubidium:
Let's say I am in the higher $>F\rangle$ state ($3$ for $^{85}\textrm{Rb}$, $2$ for $^{87}\textrm{Rb}$), how do I decay to the lowest ground ...
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1answer
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Atom interferometry,gravity and inertia: What can it measure that light interferometry can't? [closed]
What previously unexplored effects in gravity and inertia can be examined with atom interferometry in ways that hasn't already been done through light interferometry?
Can atom interferometry be used ...
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1answer
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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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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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1answer
467 views
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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1answer
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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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1answer
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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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2answers
412 views
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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1answer
92 views
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 ...
2
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1answer
87 views
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 ...
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1answer
149 views
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. ...
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1answer
204 views
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 ...
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2answers
353 views
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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1answer
91 views
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 ...
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2answers
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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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1answer
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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 ...
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1answer
670 views
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 ...
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1answer
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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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1answer
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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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1answer
173 views
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 ...
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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 ...
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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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1answer
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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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1answer
773 views
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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1answer
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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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1answer
157 views
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 ...
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1answer
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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?
