Hong and Mandel's concept of higher-order squeezing is applied to higher-harmonic generation (k\ensuremath{\ge}2). The fundamental mode is shown to be intrinsically squeezed to the order k of the process for even k and to the order of k-1 for odd k.
The concept of Nth-order squeezing and intrinsic Nth-order squeezing is introduced and applied to several physical situations that are known to exhibit second-order squeezing. It is shown that the field produced in degenerate parametric down-conversion is squeezed to all orders, as well as being intrinsically squeezed to orders 2,6,10,. . . . The same is true for the fundamental mode in second-harmonic generation within the short-time approximation, but in this case there is only intrinsic second-order squeezing. In resonance fluorescence from a two-level atom squeezing is again found to be intrinsically a second-order phenomenon, although an intrinsic second-order effect can give rise to a weak form of higher-order squeezing.
The concept of squeezing, which generally implies that one quadrature component of an optical field has measured fluctuations below the vacuum limit, is generalized to higher moments of even order. Higher-order squeezing is encountered in many of the nonlinear processes that generate second-order squeezing. It is shown that the field produced in degenerate parametric downconversion is squeezed to all even orders and is intrinsically squeezed to orders 2,6,10…. Higher-order squeezing also shows up in second harmonic generation and in resonance fluorescence from an atom. However, in those cases there is no intrinsic squeezing beyond the second order, although a strong second-order squeezing effect is manifest in the higher-order moments of the field.
The concept of 2nth-order squeezing of a quantum field is introduced as a natural generalization of the usual second-order squeezing. It is shown that the processes of degenerate parametric down conversion, harmonic generation, and resonance fluorescence all exhibit higher-order squeezing.
We consider squeezing of the electromagnetic field resulting from the interaction of the three-level ssV-shaped atom with two modes initially taken in coherent-state representation. We also consider higher-order squeezing in the sense of Hong and Mandel [Phys. Rev. Lett. 54, 323 (1985)] and then in the sense of Hillery [Phys. Rev. A 36, 3796 (1987)]. We calculate the two-mode squeezing proposed in [J. Mod. Opt. 34, 709 (1987)] and the sum squeezing defined by Hillery [Phys. Rev. A 40, 3147 (1989)] for an atom starting initially at its ground state.