Within the framework of exact quantum electrodynamics in dispersing and absorbing media, we have studied the quantum state of the radiation emitted from an initially in the upper state, prepared two-level atom in a high- $\mathit{Q}$ cavity, including the regime where the emitted photon belongs to a wave packet that simultaneously covers the areas inside and outside the cavity. For both continuing atom-field interaction and short-term atom-field interaction, we have determined the spatiotemporal shape of the excited outgoing wave packet and calculated the efficiency of the wave packet to carry a one-photon Fock state. Furthermore, we have made contact with quantum noise theories where the intracavity field and the field outside the cavity are regarded as approximately representing independent degrees of freedom such that two separate Hilbert spaces can be introduced.Within the framework of exact quantum electrodynamics in dispersing and absorbing media, we have studied the quantum state of the radiation emitted from an initially in the upper state, prepared two-level atom in a high-$\mathit{Q}$ cavity, including the regime where the emitted photon belongs to a wave packet that simultaneously covers the areas inside and outside the cavity. For both continuing atom-field interaction and short-term atom-field interaction, we have determined the spatiotemporal shape of the excited outgoing wave packet and calculated the efficiency of the wave packet to carry a one-photon Fock state. Furthermore, we have made contact with quantum noise theories where the intracavity field and the field outside the cavity are regarded as approximately representing independent degrees of freedom such that two separate Hilbert spaces can be introduced.

arXiv:0709.2998Physical Review AJul 15, 200816 citations

Quantum Electrodynamics and Quantum Optics

R. Loudon

Optica Acta International Journal of OpticsNov 1, 198511 citations

Wave-particle duality for single photons

Alain Aspect, Philippe Grangier

Hyperfine InteractionsDec 1, 198743 citations

Quantum Electrodynamics of One-Photon Wave Packets

Magdalena Stobińska, G. Alber, Gerd Leuchs

Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum state of the electromagnetic radiation field which contains a small number or even a single photon only. Despite much recent work in cavity quantum electrodynamics, which has explored this problem successfully in cases in which the number of accessible electromagnetic field modes is strongly restricted by a cavity, currently still much less is known about ideal quantum state transfer between matter and few-photon quantum states of the electromagnetic field in the extreme opposite case of free space. In this contribution we review recent work which explores characteristic quantum electrodynamical phenomena governing the interaction of a material quantum system with the electromagnetic field in extreme many-mode cases which are close to cavity-free situations. For this purpose the simplest possible quantum electrodynamical situation, namely the interaction of a single material two-level system with the wave packet of a single optical photon, is investigated in free space and in situations in which a large cavity modifies the mode structure of the electromagnetic field modes. It is demonstrated that perfect excitation of an atom by a properly shaped single-photon wave packet is possible even in free space. In particular, it is demonstrated that perfect excitation of an atom can be achieved by a single optical photon which is prepared initially in an appropriate superposition of plane-wave modes, provided this photon is focused subsequently onto the absorbing atom by a parabolic cavity.Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum state of the electromagnetic radiation field which contains a small number or even a single photon only. Despite much recent work in cavity quantum electrodynamics, which has explored this problem successfully in cases in which the number of accessible electromagnetic field modes is strongly restricted by a cavity, currently still much less is known about ideal quantum state transfer between matter and few-photon quantum states of the electromagnetic field in the extreme opposite case of free space. In this contribution we review recent work which explores characteristic quantum electrodynamical phenomena governing the interaction of a material quantum system with the electromagnetic field in extreme many-mode cases which are close to cavity-free situations. For this purpose the simplest possible quantum electrodynamical situation, namely the interaction of a single material two-level system with the wave packet of a single optical photon, is investigated in free space and in situations in which a large cavity modifies the mode structure of the electromagnetic field modes. It is demonstrated that perfect excitation of an atom by a properly shaped single-photon wave packet is possible even in free space. In particular, it is demonstrated that perfect excitation of an atom can be achieved by a single optical photon which is prepared initially in an appropriate superposition of plane-wave modes, provided this photon is focused subsequently onto the absorbing atom by a parabolic cavity.

Jan 1, 20104 citations

Spreading of Ultrarelativistic Wave Packet and Redshift

Felix M. Lev

In explaining such phenomena as the redshift and even the fact that we can see stars and planets, the effect of wave packet spreading (WPS) of the photon wave function is not taken into account. Probably the main reason is a belief that WPS is not important since a considerable WPS would blur the images more than what is seen. However, WPS is an inevitable consequence of quantum theory and moreover this effect is also known in classical electrodynamics. So it is not sufficient to just say that a considerable WPS is excluded by observations. One should try to estimate the importance of WPS and to understand whether our intuition is correct or not. We explicitly demonstrate that a standard relativistic quantum-mechanical calculation shows that spreading in the direction perpendicular to the photon momentum is very important and cannot be neglected. Hence the physics of the above phenomena is not well understood yet. Possible approaches for solving the problem are discussed.In explaining such phenomena as the redshift and even the fact that we can see stars and planets, the effect of wave packet spreading (WPS) of the photon wave function is not taken into account. Probably the main reason is a belief that WPS is not important since a considerable WPS would blur the images more than what is seen. However, WPS is an inevitable consequence of quantum theory and moreover this effect is also known in classical electrodynamics. So it is not sufficient to just say that a considerable WPS is excluded by observations. One should try to estimate the importance of WPS and to understand whether our intuition is correct or not. We explicitly demonstrate that a standard relativistic quantum-mechanical calculation shows that spreading in the direction perpendicular to the photon momentum is very important and cannot be neglected. Hence the physics of the above phenomena is not well understood yet. Possible approaches for solving the problem are discussed.

Jun 1, 20120 citations

\mathit{Q}

cavity, including the regime where the emitted photon belongs to a wave packet that simultaneously covers the areas inside and outside the cavity. For both continuing atom-field interaction and short-term atom-field interaction, we have determined the spatiotemporal shape of the excited outgoing wave packet and calculated the efficiency of the wave packet to carry a one-photon Fock state. Furthermore, we have made contact with quantum noise theories where the intracavity field and the field outside the cavity are regarded as approximately representing independent degrees of freedom such that two separate Hilbert spaces can be introduced.