Photon-number measurement states

For our first measurement we act on the photon-number entangled states in mode 3. Since the NS operation is an interference effect, it only proceeds when the entangled photons and the ancilla photon arrive at BS2 within their coherence time rcoh- In this case, the operation performs the following ... 

We can also count the total number of donor-emitted photons, or measure the corresponding analog intensity, in the presence and absence of energy transfer. From these intensities we can calculate the efficiency of energy transfer. The fluorescence intensity of the donor is proportional to the rate constant through the fluorescence pathway divided by the sum of the rates of leaving the excited state by all pathways. That is,... 

Figure 4. Conditional nonclassical state generation. Conditional (f f (.4,9) as a function of the number of detected Stokes photons. Diamonds show experimentally measured values, which are calculated from the two arms of the anti-Stokes beam-splitter via g (A.S ) = (AS AS-2)/ AS ) AS-2) (see Fig. 1 C). The measured mean photons number on the Stokes and anti-Stokes channels were fis = 1.06 and has = 0.36 respectively. The solid line shows the result of a theoretical model including background and loss on both the Stokes and anti-Stokes channels. The overall detection efficiency (a) and number of background photons (hbg ) used in the model were as = 0.35, n G = 0.27 (qas = 0.1, rdfs = 0.12) on the Stokes (anti-Stokes) channel, and were estimated from experimental measurements. For these measurements an optically-pumped 87Rb cell was used to filter the Stokes photons from the write laser. The dotted line represents < ns (AS) corrected for loss and background on the anti-Stokes channel, obtained by setting the anti-Stokes channel loss and background to zero in this model. Inset measured mean anti-Stokes number n s conditioned on the Stokes photon number ns- The solid line represents n s as predicted by the model.

We have applied the above approach to a harmonic oscillator coupled to a spin by means of a photon number - nondemolition Hamiltonian. The spin is being measured periodically, whereas the measurement outcome is ignored. For a sufficiently high measurement frequency, the state of the harmonic oscillator evolves in a unitary manner which can be influenced by a choice of the meter basis. In practice however, the time interval At between two subsequent measurements always remains finite and, therefore, the system evolution is subject to decoherence. As an example of application, we have simulated the evolution of an initially coherent state of the harmonic oscillator into a Schrodinger cat-like superposition state. The state departs from the superposition as time increases. The simulations confirm that the decoherence rate increases dramatically with the amplitude of the initial coherent state, thus destroying very rapidly all macroscopic superposition states. 

Assume that photon A (number 1) from the entangled state belongs to Alice, and photon B (number 2) to Bob. Alice and Bob introduce a common fixed coordinate system. Both photons have identical polarizations in this coordinate system, but neither Alice nor Bob knows which. Alice may measure the polarization of her photon and send this information to Bob, who may prepare his photon in that state. This, however, does not amount to teleportation because the original state could be a linear combination of the 0) (parallel) and 1) (perpendicular) states. 

There is a superposition of four three-photon states in the last row. Each state shows the state of Bob s photon (number 2 in the ket), at any given state of Alice s two photons. Finally, Alice carries out the measurement of the polarization states of her photons (1 and 3). This inevitably causes her to get (for each of the photons) either 0> or 1). This causes her to know the state of Bob s photon from the three-photon superposition [Eq. (1.25)] ... 

The one-atom maser can be used to investigate the statistical properties of non-classical light [1298, 1299]. If the cavity resonator is cooled down to T < 0.5 K, the number of thermal photons becomes very small and can be neglected. The number of photons induced by the atomic fluorescence can be measured via the fluctuations in the number of atoms leaving the cavity in the lower level n — 1). It turns out that the statistical distribution does not follow Poisson statistics, as in the output of a laser with many photons per mode, but shows a sub-Poisson distribution with photon number fluctuations 70 % below the vacuum-state limit [1300]. In cavities with low losses, pure photon number states of the radiation field (Fock states) can be observed (Fig. 9.77) [1301], with photon lifetimes as high as 0.2 s At very low... 

Since the photoabsorption measurements of Madden and Codling autoionization processes have been investigated by various methods. Excita-tion has been initiated by electrons, " by heavy particles, or by beam-foil interaction. Whereas the number of states that can be excited by photon impact is limited by selection rules, this limitation is less stringent for electron collisions, especially at low impact energies. For ion-atom or atom-atom collisions it is possible to provoke or suppress the excitation of certain types of autoionization states by careful selection of the collision partners. ... 

Another example of a teclmique for detecting absorption of laser radiation in gaseous samples is to use multiphoton ionization with mtense pulses of light. Once a molecule has been electronically excited, the excited state may absorb one or more additional photons until it is ionized. The electrons can be measured as a current generated across the cell, or can be counted individually by an electron multiplier this can be a very sensitive technique for detecting a small number of molecules excited. 

Every time an excited molecule exits the excited state region by the fluorescence pathway it emits a photon. We can either count the number of photons in a longer time interval (by a steady-state measurement of the fluorescence intensity) or make a time-resolved measurement of the fluorescence decay. These measurements can be done in an ensemble mode or on single molecules—the basic process is the same. The number of photons collected from the donor emission will be depicted by IDA and ID, where we mean the fluorescence intensity of D in the presence (Ida) and absence (ID) of acceptor. All other conditions, other than the presence or absence of acceptor, remain the same. During the same time of the experiment where we have measured the photons emitted by D, many of the excited D molecules have exited from the excited state by a pathway other than fluorescence. Obviously, the number of times a pathway has been chosen as an exit pathway is proportional to the... 

Atoms and molecules have available to them a number of energy levels associated with the allowed values of the quantum numbers for the energy levels of the atom. As atoms are heated, some will gain sufficient energy either from the absorption of photons or by collisions to populate the levels above the ground state. The partitioning of energy between the levels depends on temperature and the atom is then said to be in local thermal equilibrium with the populations of the excited states and so the local temperature can be measured with this atomic thermometer. 

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