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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Superfluid condensate wave function

I am reading Girvin's Modern Condensed Matter Physics and I have a question about the off-diagonal long-range order (ODLRO). In chapter 18.1, he starts from \begin{align} \rho(\vec{r},\vec{r}') = \...
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Definition of Parahermitian Operators

In a few situations, such as Floquet systems and Bogoliubov transformations, I have heard the terms paraunitary transformations and then parahermitian operators. What is the formal definition of these ...
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Density states of Cooper pairs

In superconductivity we can treat the electrons of a Cooper pair as a boson and electrons can occupy the same energy level. But for temperatures above $0$ K and below $T_c$ not all electrons will be ...
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How is the BCS ground state a coherent state?

A coherent state is defined as the eigenstate of the annihilation operator $\hat{a}$. It can be obtained from the vacuum of the number operator by acting with displacement operator: $$|z\rangle=\hat{D}...
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BEC Relaxation to Dispersion Minimum

I am reading this paper, which looks at the emergence of a double well dispersion in an optical lattice through shaking as in the figure below. I am curious as to what mechanism results in the atoms ...
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Conceptual doubt in Superfluidity

I'm trying to understand superfluidity from these Caltech notes on Advanced Statistical Physics (Week 1, Section IV: Landau Criterion for Superfluidity) - So far it is not clear why a moving ...
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Why does the chemical potential show up in the Gross-Pitaevskii equation?

In the case of a weakly interacting Bose-Einstein condensate the Gross-Pitaevskii equation is the motion equation that governs the evolution of the N-particle wavefunction. Starting from the Time-...
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Bose - Einstein integral together with Lorentzian distribution

I am wondering whether it is possible to solve the following integral: $$ \int\limits_{-\infty}^{\infty}d\omega \frac{1}{e^{\beta\hbar\omega}-1}\frac{1}{(\omega-\omega_0)^2+\frac{\gamma^2}{4}}$$ The ...
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Effective field theory approach to Bose-Einstein condensation

I am currently reading this paper, about an effective field theory approach to Bose-Einstein condensation. I quote We start by considering a simple non-relativistic many-body problem of spinless ...
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Extending the Sudden Approximation to 2nd quantised systems?

Background So basically there is a dictionary/correspondence between first and second quantised quantum mechanical theories. When I suddenly turn on a potential in potential in first quantised ...
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Heat capacity of Bose-Einstein Condensation

I'm studying BEC and came across this result (book "Huang K Statistical Mechanics 2 edition", page 292) Based on this expression for the internal energy: The upper value is when v>vc ...
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Fugacity of Bose-Einstein Condensation

I'm studying Bose Einstein Condensation. In the book "Huang K Statistical Mechanics 2 edition", page 288, the author gets the following result for the fugacity ($z$) as a function of ...
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Why is the variational approach in BCS theory at 0 Kelvin?

Where in the variational approach of BCS theory is it assumed to be at $T=0\: K$ (temperature). You get the energy gap equation from minimising the ground state energy but this equation is different ...
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A problem with the BCS energy expectation value of an excited state

I want to calculate the energy expectation value of the following state. \begin{align} |\Psi_{ex}\rangle = \hat{c}_{-k'\downarrow}^\dagger \hat{c}_{k''\uparrow}^\dagger \prod_{k \neq k', k''}(...
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Bose-Einstein distribution computed for negative energies?

For Bose-Einstein distribution we've $\bar{n}_{i}=\frac{g_{i}}{e^{\left(\varepsilon_{i}-\mu\right) / k_{\mathrm{B}} T}-1}$ ,$\mu \leq 0$ ( let's assume $\mu<0$). Near the origin $\frac{\varepsilon-\...
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BCS pairing and BEC pair between Fermions

In many lecture notes, it points out We can tune the scattering length, using Feshbach resonance, to realize crossover from BCS to BEC in degenerate Fermi gases. When the scattering length is ...
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Bose-Einstein condensate: anti-Helmholtz coils and temperature dependence, if one is observed

To get a Bose-Einstein condensate anti-Helmholtz coils are used to hold the BEC together. I am looking for a relationship between the strength of the magnetic field of the coils and the temperature at ...
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Does an external magnetic field help to obtain a BEC at higher temperatures than without it?

My starting point: If one takes the magnetic dipole of the electrons and not the spin as the starting point for explaining the phenomenon of Bose/Einstein condensates, one can imagine that a BEC comes ...
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Cases for a one- two- or three-dimensional structure of the Bose-Einstein condensate

The phase transition from a classical atomic gas to a Bose-Einstein condensate takes place when a critical phase space density is reached, i.e. when the density of the particles with almost the same ...
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Bosonic Bogoliubov transformation

In the Bogoliubov theory for the weakly interacting Bose gas, the Bogoliubov transformation from bosonic creation (annihilation) operators $\hat{a}_p^{(\dagger)}$ to the new set of creation (...
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Number and Types of States of Matter [closed]

I wanted to know if there were more than 5 states of matter (man-made or natural) and so I searched it up. Other than solid, liquid, gas, plasma, and Bose-Einstein state, these were varying results ...
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Kerson Huang statements about Bose-Einstein condensation

On the Kerson Huang statistical mechanics book I read, about the Bose Einstein condensate, that for temperatures higher than the condensing temperature the particles "spread thinly" over all ...
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Numerics for Bose-Hubbard model

For the Bose-Hubbard model, we know that there are the Mott insulator phase with $\langle a_i \rangle = 0$ and the superfluid phase with $\langle a_i \rangle \neq 0$. However, when we are trying to ...
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How to convert absorption/emission rate of a molecule from cross section units (or molar extinction units) to frequency units?

I try to find relation how absorption/emission rate of molecules is expressed in different types of units? For example, I found that for Rhodamine 6G the peak absorption rate (in terms of molar ...
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Describing vortices using Gross-Pitaevskii equation

A lot of the description of vortices starts by saying a vortex in a Bose-Einstein condensate can be generated by imparting an angular momentum to the container. So as I understand it is described by ...
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Why Bose-Einstein condensate is superconducting

Im looking into Quantum Computing, where the BCS Theory is used to build Qubits with a BEC. Why does the Bose-Einstein Condensate not interact with other particles and hence has no dissipation? In ...
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Relativistic Bose-Einstein Condensation (BEC)

I wonder if there is a concept similar to the one of BEC but arising from Quantum Field Theory instead that from the usual one developed in non-relativistic many-body Quantum Mechanics. In non-...
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Double Potential Well (Hubbard Model)

The Hamiltonian from the Hubbard model for the double well potential $V(x) = V_0 \frac{x^2 - q^2}{q^2}$ is given by \begin{equation} H = -J(a_L^\dagger a_R + a_R^\dagger a_L) + \frac{U}{2} (a_L^\...
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Can Bose–Einstein condensate (BEC) take up no space?

If multiple bosons can occupy the same state, does that mean you can put an infinite number of them in a fixed container at zero temperature without pressure.
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Closed form solution of the normal density of a superfluid for the Bogoliubov spectrum

I've been trying to solve the following definite integral $$ \int_0^\infty dx\, x^4\, \frac{e^{\sqrt{x^4+2 x^2}/Tp}}{\left(e^{\sqrt{x^4+2 x^2}/Tp}-1\right)^2}\, ,\quad Tp = \frac{T}{Un} $$ This is the ...
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Two different to do Bogobliubov transformation but sees to be contradictary

When try to do bogoliubov transformation on a weak-interaction cold atoms with uniform velocity $\vec{v}$, I used two different approaches, giving two different results. The Hamiltonian is $$\hat{H}=\...
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Why is Rubidium-87 used for Bose-Einstein condensates?

Rubidium-87 was the first and the most popular atom for making Bose–Einstein condensates in dilute atomic gases. Even though rubidium-85 is more abundant, rubidium-87 has a positive scattering length, ...
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Could a cloud of hydrogen-1 or helium-4 turn into Bose–Einstein condensate when the universe reaches maximum entropy?

Laboratories can cool clouds of hydrogen-1 and helium-4 respectively into Bose–Einstein condensate (BEC), while hydrogen-1 makes up 75% of all atomic matter in the observable universe and helium-4 ...
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Can multiple Helium-4 nuclei occupy the same place because the nuclei are bosonic?

A quarter of all matter in the observable universe is Helium-4 while all Helium-4 atoms have a nucleus with a zero spin integer which is characterized by Bose–Einstein statistics. Does this mean that ...
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What do scientists mean when they talk about two-dimensional photon gas in Photon BEC?

In a photon BEC, people are talking that cavity consisting of $2$ highly reflective mirrors make the photon gas $2$ dimensional by freezing out one wavevector $k_z$, which stays constant: $$ k_z=n\pi/...
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Complex Ginsburg-Landau equation for polaritons: adiabatic elimination of reservoir density

The review article 'Quantum fluids of light' focuses on exciton-polaritons in semiconductor microcavities. I don't understand the adiabatic elimination of the reservoir density $n_R$ performed on page ...
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Is Photon BEC possible in planar cavity?

It is well known result that Photon BEC was achieved in slightly curved cavity, because curved mirrors provide trapping potential (https://www.nature.com/articles/nature09567). We can see that this is ...
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What wavelengths are used practically in optical trapping?

I am currently working on my Master thesis in a cold atom research group, and have irritatingly found -- or rather not found -- that no book or paper seems to explicitly mention what wavelengths are ...
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How to observe off-diagonal long range order in superfluid?

off-diagonal long range order in superfluid is an effect that the matrix element of the single particle's density matrix remains finite in the long distance limit. My question is: how to prove this ...
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How is the phase of a BEC changing when some particles are being removed?

I have some trouble understanding what happens to the phase of a BEC when some particles are removed. The motivation of the question is the experiment of observing interference between two BECs. In my ...
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Why dilute gases do not form crystals at low temperatures?

I was wondering why a dilute gas (e.g. rubidium) forms a BEC at low temperatures rather than a crystal. My (naive) reasoning goes as follows: The dominant interaction between two atoms at low ...
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What is the Festina Lente Regime?

I am studying BEC formation without evaporative cooling, so realized only thrpugh optical means. One of the problems to face is "photon reabsorption": an atom absorbs a photon of the laser ...
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Why is a laser used to split a BEC in half?

In a youtube video, a German physicist Wolfgang Ketterle showed that two halves of the condensate creates interference pattern as though they are waves. I paused the video but still unable to ...
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Are all of the objects that composed the Bose-Einstein condensates absolutely can't be distinguished from each other?

Are all of the objects (e.g. photons or bosons) that composed Bose-Einstein condensates (BECs) literally can't be distinguished from each other? It was said several times on the Internet and many ...
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Interpretation of the condensate wavefunction

I am reading through the derivation of the Gross-Pitaevskii equation in the Heisenberg picture, and I am having some trouble interpreting the following identificiation. In the derivation the field ...
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Ideal Bose gas and Goldstone modes

In an ideal Bose gas there is a symmetry breaking phase transition, namely Bose-Einstein condensation. In a weakly interacting Bose gas or in helium-4 there is a longitudinal phonon because of the ...
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Under what conditions would neutrons pair up to produce bosons in the core of neutron star to form Bose-Einstein Condensates?

In Neutron star, the fermions get converted to bosons and form Bose-Einstein Condensates in its core. I couldn't find under what specific condition this phenomena takes place.
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Is there a difference between boson and bosonic?

I read about Bose-Einstein condensate consist of bosonic atoms at incredible low temperature do not obey Pauli exclusion, I am wondering what happens if it is possible to create fermionic photon for ...
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Why is the chemical potential of noninteracing bosons negative?

Chemical potential of noninteracting bosons is known to be negative because the Bose-Einstein distribution $[e^{(\epsilon-\mu)/T}-1]^{-1}$ should be free of singularities. However, I don't fully ...
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What does phonon exchange do in the theory of superconductivity?

In the theory of superconductivity, the phonon-mediated electron-electron scattering leads to an effective interaction, the BCS hamiltonian,$$\hat{H}_{\rm BCS}=\sum\limits_{\vec k,\sigma}\epsilon_{\...

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