Questions tagged [bose-einstein-condensate]

A Bose–Einstein condensate is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero. In this state, a large fraction of the bosons occupy the *lowest quantum state* so that macroscopic quantum phenomena are in evidence. Use for all related BEC processes.

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Does spin affect the expression for a Bose-Einstein Condensate's critical temperature?

In an assignment, we were asked to find the critical temperature of a collection of Rubidium-87 atoms. The answer used an expression derived for spin-zero bosons in Schroeder's Thermal Physics (which ...
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Why do we use grand canonical ensemble for BEC description?

The system we consider has constant $N$, $V$ and $T$ (the number of particles, volume and temperature) This is just the thermodynamic variables for the canonical ensemble, why we use fugacity $z$ or ...
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Symmetry breaking and Ginzburg-Landau theory in Charge Density Waves (CDW)

I have been thinking about this problem, but cannot get a satisfactory answer. In CDW phase, if there is Periodic Lattice Distortion (PLD, or Peierls instability), one may think of the order ...
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Quantum fields and condensates

From my fairly naive understanding of quantum field theory (QFT), a quantum field $\hat{\phi}$ is an operator field, i.e. for each spacetime point $x^{\mu}$, $\hat{\phi}(x)$ is an operator acting on ...
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Energy density in Gross-Pitaevskii equation

I guess this is a straightforward question but I was wondering if I can get an explicit steps toward the answer. Using the Gross-Pitaevskii equation: $$ \tag{1} i \hbar\frac{\partial\psi\left(x,t\...
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Reheating of the early universe and the inflaton field

I've recently been reading this set of introductory notes on the physics of reheating of the early universe. In it the author briefly mentions that, at the end of inflation, the inflaton field can be ...
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BEC interaction with light

I would like to ask when we describe coherent light interacting with atoms, what's the difference in hot atom case and BEC regime? In hot atom vapor, I know we could start with a simple interaction ...
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Bose-Einstein condensate effect

Does every boson gas go through the condensate effect? Could there be a boson gas with high energy (photons for example) that would have enough energy to be at different quantum states even at 0 K?
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Bose-Einstein Condensation at higher critical temperature

The critical temperature $T_{c}$ of a Bose-Einstein Condensate is directly proportional to $n^\frac{2}{3}$, where $n$ is the density of the system which is to be condensed. The current $T_{c}$ for ...
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How does superfluids and Bose-Einstein Condensates form?

Superfluids or Bose-Einstein Condensates can form from bosonic particles (such as the integer spin 0 $^4\mathrm{He}$) at low temperatures near absolute zero when all the bosonic particles in it start ...
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Can superfluids pass through ordinary baryonic matter?

Since superfluids consists of integer spin bosons or effective bosonic Cooper-paired fermions, Pauli Exclusion Principle does not apply to them. They can thus occupy the same quantum state as any ...
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Does Bose-Einstein Condensate other than liquid helium exist?

I have basic understanding of BEC - if you can call it understanding -, and I did a lot of reading to get it, but I never came across any examples other than liquid helium. Is it theoretically ...
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Why are Bose-Einstein Condensates (BECs) named after Bose and Einstein?

Why are Bose-Einstein Condensates (BECs) named after Bose and Einstein? What did Einstein contribute to BECs? What were the relevant papers by Bose and Einstein?
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Is Mott insulator the same as non-compressible quantum fluid?

In the field of ultracold quantum gases we study the so called Bose-Hubbard model given in second quantization: $$\hat{\mathcal{H}} = -t\sum_{\langle i,j\rangle}\hat{a}^{\dagger}_{i}\hat{a}_{j} + \...
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Long distance limit BdG-equations

Consider the dimensionless Bogoliubov-de Gennes equations for the excitations in a BEC: $$ \begin{cases} \big(-\frac{1}{2}\nabla^2+2gn({\bf r}) - \mu -\omega\big) u({\bf r})-n({\bf r})g v({\bf r}) = 0\...
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Is nanoparticle a Bose einstein Condensate

I was reading about nanopartilces(NPs) and their properties. At several places I have read that NPs act as coherent body. I wonder if the Nps can be treated as Bose Einstein condensate (BEC) as ...
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What is “Condensed Light”?

It is mentioned in this article It seems to be a Bose-Einstein condensate of some kind, but it is not exactly clear how one can create a BEC with just photons Light consists of tiny indivisible ...
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Can Bose-Einstein Condensates reflect gravitational waves?

This is a question based on the paper by Raymond Chiao in 2002 where it is stated: One of the conceptual tensions between quantum mechanics (QM) and general relativity (GR) arises from the clash ...
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If all the particles of a Bose-Einstein condensate become entangled with each other,does the system still remain a Bose-Einstein condensate?

I know that an entangled system is found in a single entangled state and that when you try to observe the individual state of a particle from an entangled system using a reduced density matrix, you ...
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Why is the symmetric phase in a Bose gas not superfluid?

In the theory of superfluidity in weakly interacting Bose gases, one finds that in the symmetric phase the exctitations have the dispersion relation $\omega = \frac{k^2}{2m}-\mu$ with gap $\Delta=-\...
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Would a collection of entangled particles behave like a superfluid? [closed]

Superfluidity of a Bose-Einstein condensate comes from the fact that all the particles are found in the same quantum state. They are described by the same macroscopic wavefunction. They never collide ...
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Is there a spontaneous $U(1)$ symmetry breaking in atomic BECs?

In the theory of Bose-Einstein condensation, one way to define the order parameter is by using the concept of spontaneous symmetry breaking. One says that, below the critical temperature, the ...
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What the difference between Bose-Einstein condensate and quantum spin liquid?

When matter gets close to absolute zero temperature, how does it becomes either BEC or QSL? I know in BEC atoms lose their individual id and becomes super-atom and as for spin liquid the alignment of ...
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Is there a classification scheme for linear classical field theories?

Central to a mathematical understanding of the Bogolyubov transformation is the study and classification of linear lattice field theories. What follows might be familiar to many people, but I just ...
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How would a BEC respond to the gravitional force of a small mass so sensitively?

Recently I watched a BBC programme on anti-gravity, most of which was wishful thinking by NASA and BAe Systems 20 years ago. At the end of the program through, they did show what appeared to be a ...
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MFT Approximation for Dilute Bose Gas

The Dilute Bose Gas has quartic Hamiltonian $$H=\sum_{k}\epsilon_k b_k^\dagger b_k+u\sum_{k\,k'q}b_{k+q}^\dagger b_{k'-q}^\dagger b_kb_{k'}.$$ It is said in a reference that Since the lowest ...
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How many particles are in the first excited state of Bose gas below critical temperature?

When Bose gas it cooled below critical temperature some of it condenses into Bose-Einstein condensate, resulting in seemingly infinite occupation of 0th state because $\mu = 0$. In reality, the 0th ...
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Thermal wavelength and critical temperature for Bose-Einstein condensate

I'm stuck with derivation of critical temperature and thermal wavelength for Bose-Einstein condensate - all sources describe equations very briefly. Suppose we have a system described by Bose-Einstein ...
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Bogoliubov-de-Gennes (BdG) formalism

Suppose you treat the mean-field BCS superconductor Hamiltonian $H$ in "BdG style" by re-writing it as $H = \frac{1}{2} \sum_k \psi_k^{\dagger} H_{BdG} \psi_k$ where, in terms of original ...
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Alternative derivation of Gross-Pitaevskii equation

I wanted to derive time-dependent Gross-Pitaevskii equation in an alternative way, but I don't know if something presented below is allowed. Hamiltonian is the following (I do not assume translational ...
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time-dependent Hartree-Fock for two-component bosons

How does the ansatz for the time-dependent Hartree-Fock wavefunction look like in second quantization if we have two-component boson system and in one case the Hamiltonian commutes with number of ...
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What is the difference between superfluidity and Bose condensation?

My question is about zero-temperature ground state of a Bose system. Suppose that the system stabilizes a BEC order parameter, say $\langle b^+ \rangle$, and fixes its phase. Is this a superfluid? And ...
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Why does the chemical potential vanish for Bose Einstein condensate?

the reasoning in a Bose Einstein condensate is to try to account for all the particles in the excited continuum states by tuning the chemical potential. However at a critical temperature $T_c$ the ...
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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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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. $$ n^{(1)},n^{(2)},...=\mathcal{O}(\mathcal{N}) $$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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The Heisenberg Uncertainty in Bose Einstein condensates

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 ...
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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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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] n_{T}(\...
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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 (...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...