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3
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2answers
192 views

Bose-Einstein condensation and phase transition

I would like to ask the following question for which I cannot find a definite answer in the literature. Of what ORDER is the phase transition leading to Bose-Einstein condensation for a ideal and ...
0
votes
1answer
38 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, $$ ...
3
votes
0answers
59 views

What are fragmented condensates?

It is defined that if more than one eigenvalue of the one-body density matrix are macroscopically occupied the condensate is said to be fragmented. $$ n^{(1)},n^{(2)},...=\mathcal{O}(\mathcal{N}) $$ ...
4
votes
1answer
168 views

Feshbach resonance in simple terms

I was reading up Feshbach resonances in cold atoms and I was unable to grasp the concept. I will tell you what I have understood. We consider two body scattering processes elastic as well as ...
0
votes
0answers
21 views

Fugacity in Bose-Einstein condensate

Just a simple question, I didn't manage to find out in my books... The fugacity $z = e^{\beta \mu}$ in the case we have condensation in a bose statistics. Is it always 1 or $z \to 1$? In the ...
1
vote
1answer
86 views

Condensate fraction and single-particle density matrix

In Bose–Einstein condensation (BEC), how to prove the largest eigenvalue of the single-particle density matrix $$\rho_{ij}=\frac{\langle\Psi|a_i^{\dagger}a_j|\Psi\rangle}{N}$$ is ...
0
votes
1answer
70 views

When will Einstein's theories become laws? [closed]

Einstein theories , specifically relativity, have been fascinating us for around 100 years yet with all the real and actual evidence of its validity we still consider it a "theory"..... How much more ...
3
votes
1answer
211 views

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 ...
1
vote
2answers
280 views

Oscillation of a Bose Einstein condensate in a harmonical trap

We were asked to try to make a theoretical description of the following phenomenon: Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency $\omega$. Suddenly the ...
2
votes
0answers
70 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. ...
6
votes
2answers
113 views

Why is chemical potential, μ=0 when calculating critical temperature of BECs?

How do we justify taking the chemical potential, $\mu$ as $0$ when calculating the critical temperature of Bose-Einstein Condensates (BECs)? I apologise as I do not how to use LaTeX, for if I did the ...
4
votes
1answer
458 views

Hamiltonians, density of state, BECs

When working with Bose-Einstein condensates trapped in potentials, how can one tell what the density of state of a system of identical bosons given the Hamiltonian, $H$? (I have been told that it is ...
1
vote
0answers
33 views

At the lambda point, why does specific heat capacity tend to infinity?

The specific heat capacity is the energy required to raise the temperature of unity mass by 1K, if at the lambda point all the bosons occupy the lowest quantum state, shouldn’t the specific heat ...
3
votes
0answers
30 views

Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
3
votes
0answers
134 views

Are gravastars observationally distinguishable from black holes?

Are observations of Hawking radiation at the acoustic event horizon in Bose-Einstein condensates consistent with gravastars? To reconcile the second law of thermodynamics with the existence of a ...
3
votes
0answers
57 views

Heisenberg uncertainty in Bose Einstein condensate

What happens to the Heisenberg uncertainty principle, when a system reaches the Bose-Einstein condensed state? In our statistical mechanics lecture, we derived the following formula for the fraction ...
0
votes
1answer
13 views

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 ...
2
votes
0answers
45 views

Numerical problem with Hartree-Fock equations for dilute Bose gas

I have to solve the following set of equations self-consistently: $$\begin{align} n_c(\mathbf{r}) & = \frac{1}{g}\left[\mu - V_{\rm ext}(\mathbf{r}) - 2 g n_{T}(\mathbf{r}) \right] \\[3mm] ...
1
vote
2answers
88 views

Laser cooling of atoms: more area or more power?

I want to optimise a Magneto-Optical trap. Laser beams come from the the x, y and z directions (positive and negative) and slow the atoms down. Would it be better to increase the beam spot-size ...
1
vote
1answer
29 views

Can you see Bose-Einstein condensates with the naked eye?

In this article it is said that "A BEC is a group of a few million atoms that merge to make a single matter-wave about a millimeter or so across." Does this mean that when they make a matter wave ...
0
votes
1answer
31 views

Unitary Bose gas

A unitary Bose gas (more about it [here]) is defined to occur when the scattering length diverges. What I don't understand, however, is which quantity/matrix is actually unitary? I mean, they could ...
0
votes
0answers
28 views

Bose-Einstein condensate in external field at finite temperature

Suppose at some finite temperature macroscopically large number of interacting bosons condense to form Bose-Einstein condensate (BEC) with some macroscopic wave function. There also exist excitations ...
0
votes
0answers
14 views

Interferometer based on atoms and gravitational field detection

I know that ultra cold atoms can be used to measure a gravitational field, but how does this work exactly. More specifically, I know that an interferometer based on atoms can be used to make very ...
0
votes
1answer
34 views

Bosonic qubits using BEC versus usual qubit implementations based on energy levels

All condensate atoms in a BEC (say like Rb, etc) effectively occupy the lowest energy-state. If it is that the case, then how are such bosons in a BEC encoded as a qubit? In particular, when Grover ...
4
votes
1answer
135 views

Bose Einstein condensation and macroscopic occupation

If have been thought, that Bose Einstein condensation occurs of the ground-state is occupied macroscopically, so $n_0\in \mathcal{O}(N)$ when performing the thermodynamic limit. So naively, this ...
-1
votes
1answer
61 views

Are there any practical applications of Mott insulators and Superfluids?

The potential applications of Bose-Einstein condensated is discussed here, I was wondering whether anyone could produce a similar argument for Superfluids and Mott insulators. EDIT: I fully realise ...
0
votes
1answer
48 views

What is the gauge field in Bose-Einstein condensation?

The Hamiltonian for bosons has $\phi^{\dagger}\phi$ terms in it which makes it U(1) invariant. Bose-Einstein Condensation apparently breaks such symmetry by choosing a definite phase, even though I ...
1
vote
1answer
42 views

How to add Langevin terms to the semiclassical Bose-Hubbard model?

I would like to add Langevin terms to the Hamilton equations of motion of the semiclassical Bose-Hubbard model. Here's what I have: I start with the standard example of Brownian motion, a particle ...
2
votes
1answer
69 views

Bogoliubov transformation [closed]

In the book "Bose-Einstein condensate", they're doing a Bogoliubov transformation: $ a_p=u_pb_p+v_{-p}^\star b_{-p}^\dagger\\ a_p^\dagger=u_p^\star b_p^\dagger+v_{-p}b_{-p} $ Where the untransformed ...
1
vote
0answers
22 views

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 ...
6
votes
0answers
122 views

What is the largest number of bosons placed in a BEC?

What is the record for the largest number of bosons placed in a Bose-Einstein condensate? What are the prospects for how high this might get in the future? EDIT: These guys reported 20 million ...
2
votes
0answers
69 views

Gross-Pitaevskii equation and Bogoliubov approach

I have a dilute weakly-interacting bose gas and make the assumption that I have only s-wave scattering. Then I'm able to write the Hamiltonian as: $$ ...
0
votes
0answers
45 views

Is a 2-atom BEC possible?

In theory, is it possible to generate a BEC with only 2 atoms? If not, what would be the lower threshold? I have a basic understanding of BECs: you consider only 2-atom interactions, pseudopotential ...
1
vote
0answers
17 views

Coupled Diff Equation from Bose Einstein distribution [closed]

I am a student doing physics hons and have had very little experience in programming. This semester we are supposed to do a computational project in thermodynamics. I have to solve these two coupled ...
0
votes
1answer
52 views

Hamiltonian of weakly-interacting Bose gas

I try to derive the Hamiltonian for a weakly-interacting Bose gas. I am stucked right now at this step, could someone explain it? Thank you! Best Michael
0
votes
0answers
21 views

Software for BEC dynamics in optical lattice

I am looking for a quantum chemistry software that deals with Bose-Einstein condensate in optical lattices (1D, 2D, 3D). I am interested in full many-body Schrodinger equation (two-body interactions - ...
0
votes
0answers
17 views

calculation of first order coherence function

I have solved a gross-pitaevskii equation for bose-einstein condensate. The wavefunction which i have obtained has the property which its square shows the number density of atoms in the condensate. ...
3
votes
0answers
53 views

Could we Bose-condense Higgs bosons?

Apart from the obvious problem that we'd have to create enough of them and somehow not let them decay, is there anything that would prevent a Higgs boson condensate?
2
votes
0answers
86 views

To what extent is the Standard Model vacuum made of a Bose-Einstein condensate of Higgs bosons?

Note: I very well understand spontaneous symmetry breaking of global symmetries and the Higgs mechanism. I want to know to what extent the Standard Model vacuum is made of a Bose-Einstein condensate ...
1
vote
1answer
32 views

BEC in interacting systems

What is your thought on the following statement: "any system of (weak/ strong) interacting bosons, in liquid phase, will form a condensate at T=0". Any example or counter-example ? Will dimensionality ...
1
vote
0answers
51 views

Is there a local canonical ensemble partition function for a Bose-Einstein gas?

The grand canonical partition function for a Bose-Einstein gas is $$ Z_{\text{grand bos}} = \exp \left( \sum_{j=0}^{\infty} -\ln \left( 1-e^{\beta(\mu-\epsilon_j)} \right)g_j \right) $$ where $\beta$ ...
0
votes
1answer
47 views

Why classical open system and Bose-Einstein condensate are not fundamentally the same?

The classical partition function for an open system is given as $$ Z_{\text{max}} = \sum_{N=0}^{\infty} \dfrac{h^{-N}}{N! } \prod_{j=1}^{N} \left( \sum_{i=0}^{\infty} e^{-\beta (E_{ij}-\mu)} g_{i} ...
0
votes
0answers
34 views

What does the particle to volume density physically mean for Bose-Eisenstein condensate?

The average number of particles $\langle N\rangle$ for a Bose-Eisenstein condensate in 3D is given as $$ \dfrac{\langle N\rangle}{V} = \dfrac{V^{-1}}{e^{\beta (0-\mu)}-1} + \int_{0}^{\infty} ...
0
votes
1answer
71 views

Why do different phases of matter coexist?

Say at a critical temperature $T_c$ there is a phase transition. If we had water, $T_c$ for the liquid-solid transition is $0 ^\circ$C. If we left a block of ice at $1 ^\circ$C for a bit, it will ...
3
votes
1answer
133 views

What does chemical potential $\mu = 0$ mean?

First off, just to be clear, the chemical potential being equal to zero is different from not having a chemical potential at all (e.g. a photon gas)? Now: physically, what does having chemical ...
0
votes
0answers
40 views

bose einstein phase transition

From Carter's book Thermodynamics and Statistical Mechanics, the partition function of a bose-einstein gas in $d$ dimensions is $$ \ln(Z) = ...
1
vote
0answers
28 views

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 ...
0
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0answers
14 views

how to show that the chemical potential goes with O(1/V)?

In statistical mechanics books $\mu=O\left(\frac{1}{V}\right)$ is being used to show the nature of the chemical potential when $T\to0$ Unfortunately, I was not able to figure out how to see how this ...
0
votes
1answer
65 views

physics of the beaker experiment for superfluid helium

here is an illustration and explanation of the beaker experiment over superfluid helium: So, according to this experiment, can anyone say what is the cause? I mean the superfluids are disconnected ...