Iwo Bialynicki-Birula and Zofia Bialynicka-Birula
We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of rho. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker representation of the solutions of the Maxwell equations in terms of just one complex function. The connection between the Bessel beams and the exponential beams is made explicit by constructing the exponential beams as wave packets of Bessel beams.
J. Phys. B vol. 39, 5545-5553 (2006) [1/2]
Showing posts with label Zofia Białynicka-Birula. Show all posts
Showing posts with label Zofia Białynicka-Birula. Show all posts
Feb 3, 2006
Nov 2, 2005
Beams of electromagnetic radiation carrying angular momentum: The Riemann–Silberstein vector and the classical–quantum correspondence
Iwo Bialynicki-Birula, and Zofia Bialynicka-Birula
All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann–Silberstein vector – a complex combination of the electric and magnetic field vectors – that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre–Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.
Opt. Commun. vol. 264, 342-351 (2006) [1/2]
All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann–Silberstein vector – a complex combination of the electric and magnetic field vectors – that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre–Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.
Opt. Commun. vol. 264, 342-351 (2006) [1/2]
Feb 16, 2005
Trojan States of Electrons Guided by Bessel Beams
Iwo Bialynicki-Birula, Zofia Bialynicka-Birula and Bartosz Chmura
Previous work [I. Bialynicki-Birula, Phys. Rev. Lett. {\bf 93}, 20402 (2004)] is extended to cover more realistic examples of electromagnetic waves, viz. the Bessel beams. It is shown that electrons may be guided by a Bessel beam with nonvanishing orbital angular momentum. The mechanism for trapping the electrons near the electromagnetic vortex line of such a wave field is the same as for the Trojan states of Rydberg electrons produced by a circularly polarized wave. The main difference is that in the present case the transverse motion of electrons in a beam is confined under the action of the electromagnetic wave alone, no additional attraction center is required. We also discuss briefly the motion of electrons in Neumann and Hankel beams.
Physics/0502025 (February 2005)
Previous work [I. Bialynicki-Birula, Phys. Rev. Lett. {\bf 93}, 20402 (2004)] is extended to cover more realistic examples of electromagnetic waves, viz. the Bessel beams. It is shown that electrons may be guided by a Bessel beam with nonvanishing orbital angular momentum. The mechanism for trapping the electrons near the electromagnetic vortex line of such a wave field is the same as for the Trojan states of Rydberg electrons produced by a circularly polarized wave. The main difference is that in the present case the transverse motion of electrons in a beam is confined under the action of the electromagnetic wave alone, no additional attraction center is required. We also discuss briefly the motion of electrons in Neumann and Hankel beams.
Physics/0502025 (February 2005)
Aug 29, 2003
Vortex lines of the electromagnetic field
Iwo Bialynicki-Birula and Zofia Bialynicka-Birula
A new method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann–Silberstein vector is multiplied by a complex scalar function . Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeros of the function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.
Phys. Rev. A vol. 67, 062114-1-8 (2003)
A new method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann–Silberstein vector is multiplied by a complex scalar function . Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeros of the function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.
Phys. Rev. A vol. 67, 062114-1-8 (2003)
Jan 21, 2002
Center-of-mass motion in the many-body theory of Bose-Einstein condensates
Iwo Białynicki-Birula and Zofia Białynicka-Birula
The method of generating a family of new solutions starting from any wave function satisfying the nonlinear Schrödinger equation in a harmonic potential proposed recently [J. J. García-Ripoll, V. M. Pérez-García, and V. Vekslerchik, Phys. Rev. E 64, 056602 (2001)] is extended to the many-body theory of mutually interacting particles. Our method is based on a generalization of the displacement operator known in quantum optics, and results in the separation of the center-of-mass motion from the internal dynamics of many-body systems. The center-of-mass motion is analyzed for an anisotropic rotating trap and a region of instability for intermediate rotational velocities is predicted.
Phys. Rev. A 65, 063606 (2002)
The method of generating a family of new solutions starting from any wave function satisfying the nonlinear Schrödinger equation in a harmonic potential proposed recently [J. J. García-Ripoll, V. M. Pérez-García, and V. Vekslerchik, Phys. Rev. E 64, 056602 (2001)] is extended to the many-body theory of mutually interacting particles. Our method is based on a generalization of the displacement operator known in quantum optics, and results in the separation of the center-of-mass motion from the internal dynamics of many-body systems. The center-of-mass motion is analyzed for an anisotropic rotating trap and a region of instability for intermediate rotational velocities is predicted.
Phys. Rev. A 65, 063606 (2002)
Jul 26, 2001
Motion of vortex lines in nonlinear wave mechanics
Iwo Białynicki-Birula and Zofia Białynicka-Birula
We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula, and C. Śliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schrödinger equation with harmonic forces. We also argue that under certain conditions, the influence of the contact nonlinearity on the motion of vortex lines is negligible. The present analysis adds new weight to our previous conjecture that the topological features of vortex dynamics are to a large extent universal.
Phys. Rev. A 65, 014101 (2002)
We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula, and C. Śliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schrödinger equation with harmonic forces. We also argue that under certain conditions, the influence of the contact nonlinearity on the motion of vortex lines is negligible. The present analysis adds new weight to our previous conjecture that the topological features of vortex dynamics are to a large extent universal.
Phys. Rev. A 65, 014101 (2002)
Jul 12, 2000
Squeezing of electromagnetic field in a cavity by electrons in Trojan states
Piotr Kochański, Zofia Bialynicka-Birula, and Iwo Bialynicki-Birula
The notion of the Trojan state of a Rydberg electron, introduced by I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly [Phys. Rev. Lett. 73, 1777 (1994)] is extended to the case of an electromagnetic field quantized in a cavity. The shape of the electronic wave packet describing the Trojan state is practically the same as in the previously studied externally driven system. The fluctuations of the quantized electromagnetic field around its classical value exhibit strong squeezing. The emergence of Trojan states in the cylindrically symmetrical system is attributed to spontaneous symmetry breaking.
Phys. Rev. A 63, 013811 (2001)
The notion of the Trojan state of a Rydberg electron, introduced by I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly [Phys. Rev. Lett. 73, 1777 (1994)] is extended to the case of an electromagnetic field quantized in a cavity. The shape of the electronic wave packet describing the Trojan state is practically the same as in the previously studied externally driven system. The fluctuations of the quantized electromagnetic field around its classical value exhibit strong squeezing. The emergence of Trojan states in the cylindrically symmetrical system is attributed to spontaneous symmetry breaking.
Phys. Rev. A 63, 013811 (2001)
Jun 1, 1999
Motion of vortex lines in quantum mechanics
Iwo Bialynicki-Birula, Zofia Bialynicka-Birula and Cezary Śliwa
Exact analytic solutions of the time-dependent Schrödinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.
Phys. Rev. A 61, 032110 (2000)
Exact analytic solutions of the time-dependent Schrödinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.
Phys. Rev. A 61, 032110 (2000)
Jun 16, 1997
Radiative decay of Trojan wave packets
Zofia Bialynicka-Birula and Iwo Bialynicki-Birula
We calculate the decay rates due to spontaneous emission for electronic states described by Trojan wave packets. The spontaneous decay rate for a typical Trojan state (n=60) is six orders of magnitude smaller than the ionization rate and it is about one order of magnitude smaller than the rate for the corresponding ordinary circular Rydberg state.
Phys. Rev. A 56, 3623 (1997)
We calculate the decay rates due to spontaneous emission for electronic states described by Trojan wave packets. The spontaneous decay rate for a typical Trojan state (n=60) is six orders of magnitude smaller than the ionization rate and it is about one order of magnitude smaller than the rate for the corresponding ordinary circular Rydberg state.
Phys. Rev. A 56, 3623 (1997)
Nov 5, 1996
Rotational frequency shift
Iwo Bialynicki-Birula and Zofia Bialynicka-Birula
The notion of the rotational frequency shift, an analog of the Doppler shift, is introduced. This new frequency shift occurs for atomic systems that lack rotational invariance, but have stationary states in a rotating frame. The rotational frequency shift is given by the scalar product of the angular velocity and the angular momentum of the emitted photon in full analogy with the standard Doppler shift which is given by the scalar product of the linear velocity of the source and the linear momentum of the photon. The rotational frequency shift can be observed only in a Mössbauer-like regime when the angular recoil is negligible.
Phys. Rev. Lett. 78, 2539 (1997)
The notion of the rotational frequency shift, an analog of the Doppler shift, is introduced. This new frequency shift occurs for atomic systems that lack rotational invariance, but have stationary states in a rotating frame. The rotational frequency shift is given by the scalar product of the angular velocity and the angular momentum of the emitted photon in full analogy with the standard Doppler shift which is given by the scalar product of the linear velocity of the source and the linear momentum of the photon. The rotational frequency shift can be observed only in a Mössbauer-like regime when the angular recoil is negligible.
Phys. Rev. Lett. 78, 2539 (1997)
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