Generation of highly nonclassical n-photon polarization states by superbunching at a photon bottleneck Holger F. Hofmann * PRESTO, Japan Science and Technology Corporation (JST), Research Institute for Electronic Science, Hokkaido University, Kita-12 Nishi-6, Kita-ku, Sapporo 060-0812, Japan (Received 27 November 2003; revised manuscript received 26 May 2004; published 24 August 2004) It is shown that coherent superpositions of two oppositely polarized n-photon states can be created by postselecting the transmission of n independently generated photons into a single-mode transmission line. It is thus possible to generate highly nonclassical n-photon polarization states using only the bunching effects associated with the bosonic nature of photons. The effects of mode-matching errors are discussed and the possibility of creating n-photon entanglement by redistributing the photons into n separate modes is considered. DOI: 10.1103/PhysRevA.70.023812 PACS number(s): 42.50.Dv, 03.67.Mn, 42.50.Ar I. INTRODUCTION The creation of highly nonclassical states is one of the fundamental challenges in quantum optics. In particular, multiphoton entanglement and superpositions of macroscopi- cally distinguishable states (commonly referred to as cat states, after Schrödinger’s famous cat paradox [1]) may be very useful as resources for optical quantum-information processes such as teleportation, cloning, or quantum compu- tation [2–7]. Recently, it has been shown that multiphoton entanglement can indeed be created and manipulated using only single-photon sources, beam splitters, and postselection based on precise photon detection [8–15]. In previous inves- tigations, these methods have been applied to photonic qu- bits, where the goal was to obtain exactly one photon per spatial mode. In order to achieve this kind of output, it is necessary to discard the cases where several photons bunch up in a single spatial mode as unwanted errors. However, it is also possible to specifically select cases where several pho- tons bunch up in the same mode. In particular, this method has been used to propose the generation of spatial mode en- tanglement [16,17]. In the following, a related proposal is presented for the generation of highly nonclassical polarization states. It is shown that a coherent superposition of two oppositely polar- ized n-photon polarization states can be obtained by trans- mitting n independently generated photons with homoge- neously distributed polarizations into a single spatial mode. For large photon numbers, this n-photon polarization state has the nonclassical statistical properties of a cat state, since the superposition is between two well separated regions of the Poincaré sphere [18] and the two polarization states can be distinguished by measuring only a few photons. On the other hand, highly nonclassical interference effects between the two components of the superposition will be observable in the polarization statistics of the Stokes vector components orthogonal to the polarization along which the superposition is prepared [19]. Once a cat-state superposition of polarization states is re- alized in a single mode, it is also possible to generate the corresponding multiparticle entangled state by redistributing the photons into separate channels, effectively transforming the local state of n photons in one spatial mode into an en- tangled state of n photons in n spatial modes. In the present proposal, the photons are then transferred from n input modes to n output modes through a single-mode bottleneck. The quantum interference effects associated with the bosonic nature of photons leads to a superbunching effect in the po- larization, resulting in maximal n-photon entanglement in the output. It is thus possible to realize a strong interaction be- tween an arbitrarily large number of photons by temporarily bunching them into a single-mode channel. The superbunch- ing effect at a photon bottleneck may therefore be a useful tool in the realization of a wide range of multiphoton quan- tum operations. II. THE SUPERBUNCHING EFFECT The bunching effect used to obtain the nonclassical polar- ization state can be understood by considering the analogy with two-photon bunching. If a horizontally polarized photon and a vertically polarized photon are transmitted into the same spatial mode, their circular polarizations will always be the same—either both right polarized or both left polarized. Quantum interference removes the component with different circular polarization. This effect can be generalized to n pho- tons by choosing a homogeneous distribution of linear polar- ization angles. The quantum interference between the differ- ent linear single-photon polarizations then removes all components of the circular polarization, except for the two components where all photons have the same circular polar- ization. However, quantum coherence between the two maxi- mally polarized cases is preserved since the bunching effect does not distinguish between right or left circular polariza- tion. The validity of this argument can be verified by defining the following n-photon input state: *Present address: Graduate School of Advanced Sciences of Mat- ter, Hiroshima University, Kagamiyama 1-3-1, Higashi Hiroshima 739-8530, Japan. Electronic address: h.hofmann@osa.org PHYSICAL REVIEW A 70, 023812 (2004) 1050-2947/2004/70(2)/023812(7)/$22.50 ©2004 The American Physical Society 70 023812-1