what is the difference between two? does multimode photon means a wave packet which contains waves of electric field oscillating at different frequencies ? and single mode photons have one wave oscillating at one frequency?
This is a quantum optics question. The classical electromagnetic states are typically called "coherent" and are very special combinations of photons. In general, an N photon state can be a crazily correlated as an N electron state so that no 3D picture of the system is adequate. You can have mixtures of N photons that have well defined photon number with different frequencies but this is often not the case.
thanks Clifford
can you refer to some literature for detailed understanding
I've never been exceptionally happy with any of the quantum books on correlations because they are very formal involving Fock space. I allude to some of the problem in my PhD thesis from a geometric point of view but it really deserves a short intuitive treatment. The book The Quantum Theory of Light by Loudon is a standard.
A mode is a normalized, complex square integrable function together with two free (real) parameters, namely one complex amplitude A. Note that a single mode can cover many frequencies! The classical electric field would correspond to the real part of this function. You can have a single excitation (photon) of such a mode. This could for example be a Gaussian pulse with a certain width tau with a certain center frequency w0 and a certain center time t0 according to E(t)=Re{ A* exp(-(t-t0)^2 / (2 tau^2)) *exp(-i w0 t) } (I omitted the canonical normalisation here). But it could also be a function that involves two Gaussians or ten Gaussians of various relative amplitudes and two triangles or squares of various size or duration, whatever you like, but only with one global amplitude A. If you devise an interferometric experiment that measures A, you will find that x=Re{A} and p=Im {A} are two non-commuting variables, called the quadratures. If you have a single photon in this single mode, you will find a bimodal probability distribution if you measure x or p. Just like the probability distribution of a harmonic oscillator in the first excited state. If you devise a measurement that measures the energy, proportional to A^2=x^2+p^2, you measure how many photons this mode contains. A detector that covers this mode will click exactly once (if it is 100% efficient). A multimode photon is a mixed state where a photon can be in different such modes, associated with several independent amplitudes A,B,C etc. These could also be two Gaussian pulses. But in this case it is impossible to devise a measurement such that a single quadrature x is measured with a probability distribution according to the first excited oscillator state. Because in each run of the experiment, the photon would be in either of the two Gaussians. It sounds as if this is the case in the single mode of two Gaussians as well, but the difference is revealed in such a quadrature measurement. A multimode photon state is essentially one where you know that it is exactly one photon, but you don't know it's mode, because you don't know what the sender of this photon is doing exactly. I hope this helps.
I think the single mode photon will one step(absorb or release aphoton),but the multimode photon will a proess what a partil form the initial state to the final state have two and more proess of the absorbing or releaseing a photon. The single mode and multimode photon is correspond to different the Feynman diagram .
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