We address the problem of identifying the dynamical variables representing the phase of a quantum field by analyzing what is measured in two simple homodyne experiments. This leads us to identify operators CM.SM corresponding to the measured cosine and sine of the phase difference. The predictions of the theory are tested in an experiment in which the input fields are derived from a highly stable He:Ne laser. Photon-counting measurements extending from mean photon numbers 30 down to 10"" show good agreement between theory and experiment. The implications for identifying the "correct" phase operator are briefly discussed. PACS numbers: 42.50.Wm, 03.65.Bz sinlThe question of which is the proper dynamical variable corresponding to the phase of a quantum field has been the subject of discussion and controversy for a long time. The problem appeared to be solved by the introduction of two Hermitian dynamical variables analogous to the sine and cosine of the phase [1,2], but as the two variables do not commute, this has tended to be regarded as an unsatisfactory solution.There have been numerous attempts to construct other, more satisfactory phase operators [3-13], and we mention particularly the recent extensive work of Pegg and Barnett [9-11], A few experiments [14][15][16] were also reported in which phase differences and their fluctuations were measured as a function of average photon number, and attempts were made to test some of the definitions against experiments [17][18][19][20][21], but no clear conclusion emerged.We have approached the phase problem in a diff'erent, more operational way, by analyzing what is actually measured in a typical homodyne experiment to determine the phase diff'erence between two fields, both in classical and in quantum optics [22]. This leads to different dynamical variables CM^SM representing the cosine and sine of the measured phase difference for different experiments. We examine two measurement schemes for extracting the phase, which have been considered before [23][24][25][26][27][28][29][30]. For comparison we then present the results of experiments in which the phase difference between two coherent fields is measured for mean detected photon numbers im) ranging from =30 down to = 10~l This range extends more than 2 orders of magnitude beyond that of previously reported phase measurements.Classical theory.-Measurements of the phase difference between two light beams are generally based on some kind of interference or homodyne (or heterodyne) experiment like that shown in Fig. 1. Two incoming light beams are mixed by a 50:50 beam splitter BS, resulting in mixed signals of intensities hJ^ emerging from the two exit ports. The numbers of photoelectric pulses mj^m^ detected by two similar photodetectors D3,D4 of quantum efficiency a in some counting time interval T are registered. When the numbers rrij are large, they are representative of the integrated light intensity Wj 1426 © 1991 The American Physical Society ^aSl^^Ij{t')dt' 0=3,4). Within the domain of classical optics ...

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Extracellular ATP has recently been identified as an important regulator of cell death in response to pathological insults. When SN4741 cells, which are dopaminergic neurons derived from the substantia nigra of transgenic mouse embryos, are exposed to ATP, cell death occurs. This cell death is associated with prominent cell swelling, loss of ER integrity, the formation of many large cytoplasmic vacuoles, and subsequent cytolysis and DNA release. In addition, the cleavage of caspase-3, a hallmark of apoptosis, is induced by ATP treatment. However, caspase inhibitors do not overcome ATP-induced cell death, indicating that both necrosis and apoptosis are associated with ATP-induced cell death and suggesting that a necrotic event might override the apoptotic process. In this study we also found that P2X 7 receptors (P2X 7 Rs) are abundantly expressed in SN4741 cells, and both ATP-induced swelling and cell death are reversed by pretreatment with the P2X 7 Rs antagonist, KN62, or by knock-down of P2X 7 Rs with small interfering RNAs. Therefore, extracellular ATP release from injured tissues may act as an accelerating factor in necrotic SN4741 dopaminergic cell death via P2X 7 Rs. Parkinson disease (PD)2 is an idiopathic neurodegenerative disorder characterized by selective cell death of dopaminergic neurons in the substantia nigra (1). The symptoms of PD only become apparent when more than 50% of the dopaminergic neurons in the substantia nigra pars compacta are lost, which leads to an over 80% reduction in dopamine levels in the striatum (2). Epidemiological studies and pathological analyses demonstrate that sporadic PD with late onset occurs in 95% of patients, whereas the remaining 5% of PD cases are familial diseases with early onset (1, 2). Although the etiological causes of PD have not been fully elucidated, several factors have been suggested as causes of neuronal degeneration. These include environmental toxins, genetic factors, and mitochondrial dysfunction as well as proteasomal impairment and oxidative stress (3). Recently, however, there has been increasing recognition of the possible role of neuro-inflammation as a major factor in the pathogenesis of PD (4). The inflammatory component is an attractive target for therapeutic intervention. It is now generally accepted that high levels of extracellular ATP may be released under pathological conditions such as inflammation, trauma, and stress. The role of extracellular ATP and purinergic receptors in neurodegeneration is one of the focus areas of cell death research (5).P2X 7 receptors (P2X 7 Rs) are unusual purinergic receptors in that they can exist in two functional states: either as cationselective channels or as nonselective pores (6). The permeability transition of P2X 7 Rs from channel to pore occurs either upon sustained stimulation with high ATP concentrations or repeated pulses of ATP application (7). Seven members of the P2X receptor family have been cloned that share the same predicted structure with two transmembrane-spanning domains. These are a...

Excitotoxicity and oxidative stress mediate neuronal death after hypoxic-ischemic brain injury. We examined the possibility that targeting both N-methyl-D-aspartate (NMDA) receptor-mediated excitotoxicity and oxidative stress would result in enhanced neuroprotection against hypoxicischemia. 2-Hydroxy-5-(2,3,5,6-tetrafluoro-4-trifluoromethyl-benzylamino)-benzoic acid (Neu2000) was derived from aspirin and sulfasalazine to prevent both NMDA neurotoxicity and oxidative stress. In cortical cell cultures, Neu2000 was shown to be an uncompetitive NMDA receptor antagonist and completely blocked free radical toxicity at doses as low as 0.3 lmol/L. Neu2000 showed marked neuroprotection in a masked fashion using histology and behavioral testing in two rodent models of focal cerebral ischemia without causing neurotoxic side effects. Neu2000 protected against the effects of middle cerebral artery occlusion, even when delivered 8 h after reperfusion. Single bolus administration of the drug prevented gray and white matter degeneration and spared neurologic function for over 28 days after MACO. Neu2000 may be a novel therapy for combating both NMDA receptor-mediated excitotoxicity and oxidative stress, the two major routes of neuronal death in ischemia, offering profound neuroprotection and an extended therapeutic window.

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