72
3 Light–Matter Interactions for Photonic Applications
Fig. 3.5 Schematic 2D diagram of the physics behind Bose–Einstein condensation (BEC), showing
the impact of the mass on the critical temperature. Boxes illustrate the formation of a condensate
from a dilute gas of massive bosons for different temperatures and masses. From left to right, the
temperature decreases towards the absolute zero point (0 K). From top to bottom, the particle mass
(an effective one for quasi-particles) is decreased. For a given mass configuration (row), the critical temperature for BEC is highlighted by a thick-lined box. At elevated temperatures, the gas
of particles obeys the classical Boltzmann statistics. By decreasing the temperature, an increased
matter–wave overlap is obtained according to the growing particle de-Broglie wavelength λ dB .
Below a critical temperature T critical , a condensate is formed, whereas the ideal gas of bosons is
described by the Bose–Einstein distribution function. Note that the majority of particles is in the
same quantum degenerate state and described by the same wave-function, rendering the condensed
particles indistinguishable. Hence a macroscopically-occupied state with phase-coherent population
due to a spontaneous symmetry break is a key signature of BEC. At finite temperatures, a minority
of uncondensed particles coexists, expressed by the condensate fraction n 0 /n total (ground-state over
total particle density). Note the similarity to superfluidity, with normal and superfluid phase coexisting. In contrast, at 0 K, all particles occupy one (ground) state forming a pure Bose condensate.
Heavier bosons at given temperature overlap less than the lighter ones due to their shorter λ dB .
Thus, by reducing the mass, at given temperature, the critical conditions can be met; or expressed
in a more practical way, lighter particles enable condensation studies at elevated temperatures. For
bosons with mass of the order of the free electron mass m 0 , T critical ≈ mK. This scheme is inspired
by the original (1D) chart created by Ketterle and used on his research group’s online representation
[132], and practically extended to a reduced form of the author’s 3D chart shown in [9] (Chap.1
therein), which even shows a third axis (density n) involving the critical particle density n critical
3 Light–Matter Interactions for Photonic Applications
Fig. 3.5 Schematic 2D diagram of the physics behind Bose–Einstein condensation (BEC), showing
the impact of the mass on the critical temperature. Boxes illustrate the formation of a condensate
from a dilute gas of massive bosons for different temperatures and masses. From left to right, the
temperature decreases towards the absolute zero point (0 K). From top to bottom, the particle mass
(an effective one for quasi-particles) is decreased. For a given mass configuration (row), the critical temperature for BEC is highlighted by a thick-lined box. At elevated temperatures, the gas
of particles obeys the classical Boltzmann statistics. By decreasing the temperature, an increased
matter–wave overlap is obtained according to the growing particle de-Broglie wavelength λ dB .
Below a critical temperature T critical , a condensate is formed, whereas the ideal gas of bosons is
described by the Bose–Einstein distribution function. Note that the majority of particles is in the
same quantum degenerate state and described by the same wave-function, rendering the condensed
particles indistinguishable. Hence a macroscopically-occupied state with phase-coherent population
due to a spontaneous symmetry break is a key signature of BEC. At finite temperatures, a minority
of uncondensed particles coexists, expressed by the condensate fraction n 0 /n total (ground-state over
total particle density). Note the similarity to superfluidity, with normal and superfluid phase coexisting. In contrast, at 0 K, all particles occupy one (ground) state forming a pure Bose condensate.
Heavier bosons at given temperature overlap less than the lighter ones due to their shorter λ dB .
Thus, by reducing the mass, at given temperature, the critical conditions can be met; or expressed
in a more practical way, lighter particles enable condensation studies at elevated temperatures. For
bosons with mass of the order of the free electron mass m 0 , T critical ≈ mK. This scheme is inspired
by the original (1D) chart created by Ketterle and used on his research group’s online representation
[132], and practically extended to a reduced form of the author’s 3D chart shown in [9] (Chap.1
therein), which even shows a third axis (density n) involving the critical particle density n critical