We compare four-wave mixing in quantum degenerate gases of bosonic and fermionic atoms. We find that matter-wave gratings formed from either bosonic or fermionic atoms can in principle exhibit nearly identical Bragg scattering and four-wave mixing properties. This implies that effects such as coherent matter-wave amplification and superradiance can occur in degenerate Fermi gases. This effect is due to constructive many-particle quantum interferences, which in the boson case are interpreted as "Bose enhancement."We compare four-wave mixing in quantum degenerate gases of bosonic and fermionic atoms. We find that matter-wave gratings formed from either bosonic or fermionic atoms can in principle exhibit nearly identical Bragg scattering and four-wave mixing properties. This implies that effects such as coherent matter-wave amplification and superradiance can occur in degenerate Fermi gases. This effect is due to constructive many-particle quantum interferences, which in the boson case are interpreted as "Bose enhancement."

arXiv:cond-mat/0008264Physical Review LettersMay 7, 200162 citations

Enhancement of near-resonant degenerate four-wave-mixing signals by excitation of a coupled transition

A. D. Wilson‐Gordon, Harry Friedmann

It is shown that intense collisionless Rayleigh-type extraresonant signals in degenerate four-wave mixing (DFWM) can be obtained when the $| a 〉\ensuremath{\rightarrow}| b 〉$ transition which produces the DFWM signal is coupled to another transition ($ | a 〉\ensuremath{\rightarrow}| d 〉$) which is excited near-resonantly by an additional laser beam. Two effects contribute to the Rayleigh-type extraresonant signal at ${\ensuremath{\omega}}_{2}={\ensuremath{\omega}}_{1}$. The first effect is resonance-enhanced three-photon scattering (TPS), which leads to the population of state $| b 〉$ and consequently contributes a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$, the off-diagonal density-matrix element, which is characterized by the linewidth ${(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$ , the inverse lifetime of the state $| b 〉$ . The second effect derives from the effective lifetime acquired by the ground state $| a 〉$ due to its strong coupling to state $| d 〉$ . This leads to a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$ characterized by a linewidth $\frac{1}{2}{(\frac{1}{{T}_{1}})}_{\mathrm{da}}$ , which is half the inverse lifetime of the state $| d 〉$ . When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\gg}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the TPS effect dominates and the extraresonant DFWM signal is narrow and intense. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\simeq}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the signal is less intense and interference between the two effects is evident.It is shown that intense collisionless Rayleigh-type extraresonant signals in degenerate four-wave mixing (DFWM) can be obtained when the $| a 〉\ensuremath{\rightarrow}| b 〉$ transition which produces the DFWM signal is coupled to another transition ($ | a 〉\ensuremath{\rightarrow}| d 〉$) which is excited near-resonantly by an additional laser beam. Two effects contribute to the Rayleigh-type extraresonant signal at ${\ensuremath{\omega}}_{2}={\ensuremath{\omega}}_{1}$. The first effect is resonance-enhanced three-photon scattering (TPS), which leads to the population of state $| b 〉$ and consequently contributes a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$, the off-diagonal density-matrix element, which is characterized by the linewidth ${(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the inverse lifetime of the state $| b 〉$. The second effect derives from the effective lifetime acquired by the ground state $| a 〉$ due to its strong coupling to state $| d 〉$. This leads to a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$ characterized by a linewidth $\frac{1}{2}{(\frac{1}{{T}_{1}})}_{\mathrm{da}}$, which is half the inverse lifetime of the state $| d 〉$. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\gg}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the TPS effect dominates and the extraresonant DFWM signal is narrow and intense. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\simeq}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the signal is less intense and interference between the two effects is evident.

Physical Review ASep 1, 19845 citations

Rayleigh scattering in a dense spin-polarized gas

T. Andreeva, P. L. Rubin, Evgenii A. Yukov

Journal of Experimental and Theoretical PhysicsApr 1, 19950 citations

| b 〉

and consequently contributes a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$, the off-diagonal density-matrix element, which is characterized by the linewidth

{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}

, the inverse lifetime of the state

| b 〉

. The second effect derives from the effective lifetime acquired by the ground state

| a 〉

due to its strong coupling to state

| d 〉

. This leads to a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$ characterized by a linewidth

\frac{1}{2}{(\frac{1}{{T}_{1}})}_{\mathrm{da}}

, which is half the inverse lifetime of the state

| d 〉

. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\gg}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the TPS effect dominates and the extraresonant DFWM signal is narrow and intense. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\simeq}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the signal is less intense and interference between the two effects is evident.