We have constructed a novel optical trap for neutral atoms by using a Laguerre-Gaussian (doughnut) beam whose frequency is blue detuned to the atomic transition. Laser-cooled rubidium atoms are trapped in the dark core of the doughnut beam with the help of two additional laser beams which limit the atomic motion along the optical axis. About 10 8 atoms are initially loaded into the trap, and the lifetime is 150 ms. Because the atoms are confined at a point in a weak radiation field in the absence of any external field, ideal circumstances are provided for precision measurements. The trap opens the way to a simple technique for atom manipulation, including Bose-Einstein condensation of gaseous atoms.[S0031-9007 (97)03456-X] PACS numbers: 32.80.Pj, 39.90. + d

We investigate controlled phase separation of a binary Bose-Einstein condensate (BEC) in the proximity of mixed-spin-channel Feshbach resonance in the |F = 1, mF = +1 and |F = 2, mF = −1 states of 87 Rb at a magnetic field of 9.10 G. Phase separation occurs on the lower magnetic-field side of the Feshbach resonance while the two components overlap on the higher magnetic-field side. The Feshbach resonance curve of the scattering length is obtained from the shape of the atomic cloud by comparison with the numerical analysis of coupled Gross-Pitaevskii equations.

We experimentally studied the spin-dependent collision dynamics of 87 Rb spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the ͉F =2,m F =0͘ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to 3.0 G. The atom loss rate due to inelastic two-body collisions was found to be 1.4͑2͒ ϫ 10 −13 cm 3 s −1 . Spin mixing in the F = 2 manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each m F component.

We report an experimental quantum key distribution that utilizes balanced homodyne detection, instead of photon counting, to detect weak pulses of coherent light. Although our scheme inherently has a finite error rate, it allows high-efficiency detection and quantum state measurement of the transmitted light using only conventional devices at room temperature. When the average photon number was 0.1, an error rate of 0.08 and "effective" quantum efficiency of 0.76 were obtained.PACS numbers: 03.67. Dd, 42.50.Lc According to quantum mechanics, one cannot obtain information about a single quantum system without disturbing its state [1] nor can one clone an unknown state [2]. Quantum cryptography is a technique for realizing secure communications exploiting these principles. The most popular protocol is quantum key distribution (QKD) in which two non-orthogonal states (B92 protocol) [3] or four states (BB84 protocol) [4] are sent via a quantum channel in order to generate random keys owned only by the legitimate sender (usually called Alice) and the receiver (Bob). These keys are then used to encode messages.In practice, a faint laser pulse is usually used as the quantum system, and keys are encoded by its polarization or its phase. Ideally, a single photon is desirable, but it is very difficult to generate it experimentally. Most of the previous experimental and theoretical studies on QKD used or postulated photon counting as a means to detect weak light. However, the usage of photon counting gives rise to two limitations. One is a technical limitation that at present there exists no efficient photon counter for infrared light, especially for 1.55-µm where optical loss in an optical fiber is minimum. State-of-the-art experiments used a specially designed photon-counting system made up of cooled avalanche photo diode operated in a gated Geiger mode [5][6][7]. For example, a quantum efficiency of 7% for 1.55µm with a dark-count probability of 10 −4 per 2.6-nsec time-window was reported [8]. Another limitation is a more fundamental: the quantum state of the transmitted light cannot be directly measured; the state alternation is inferred only from the change of the error rate. For example, when the eavesdropper (usually called Eve) changes the photon number distribution of the transmitted light while keeping the polarization (or the phase) and the mean photon number, Bob cannot notice the presence of Eve. This feature allows Eve to perform many kinds of attacks and leads to security holes (one example is the photon number splitting attack [9]). * Electronic address: hirano@qo.phys.gakushuin.ac.jpIn this paper, we propose using balanced homodyne detection for implementing the BB84 protocol with phase coding [10]. As we will explain, the above limitations associated with photon counting can be resolved by using balanced homodyne detection. In order to demonstrate the experimental feasibility of our scheme, we have performed QKD by sending light pulses at 1.55-µm wavelength through an optical fiber of 20-cm length. Whe...

In this letter, first, we investigate the security of a continuous-variable quantum cryptographic scheme with a postselection process against individual beam splitting attack. It is shown that the scheme can be secure in the presence of the transmission loss owing to the postselection. Second, we provide a loss limit for continuous-variable quantum cryptography using coherent states taking into account excess Gaussian noise on quadrature distribution. Since the excess noise is reduced by the loss mechanism, a realistic intercept-resend attack which makes a Gaussian mixture of coherent states gives a loss limit in the presence of any excess Gaussian noise.The security of quantum cryptography is degraded by the presence of realistic experimental imperfections. In particular the transmission loss limits the performance of schemes for a long distance transmission [1].Recently several continuous-variable quantum cryptographic schemes have been proposed [2,3,4,5,6,7,8,9]. Those are sorted into either all-continuous type or hybrid type [5], the all-continuous scheme distributes a continuous key and the hybrid scheme distributes a discrete key. A loss limit, in the sense that the mutual information between Alice and Bob I AB cannot be greater than the Shannon information of an Eavesdropper (Eve) I E , is given for an all-continuous scheme [6] and it is shown that this limitation can be removed by introducing a postselection process for a hybrid scheme [7,8,9]. The existence of loss limit is an open question.The reliable security measure for discrete quantum cryptographic schemes against individual attacks is the secure key gain G which ensures that I E can be arbitrarily small in the long key limit if G is positive [10,11]. The question is how high G can be for a given loss or transmission distance in realistic conditions. The estimations are given for BB84 protocol [11], entangled photon protocol [12], and B92 protocol [13]. The estimation of G for continuous schemes, if possible, is important as a comparison with discrete schemes. At least, the framework [14,15] can be adapted to hybrid schemes.For these discrete schemes, the experimental imperfections are mostly determined by observed bit error rate and dark count rate of single photon detectors [11,12,13]. In continuous-variable schemes, the experimental imperfections appear as the change of quadrature distributions. Experimentally, quadrature measurement is performed slightly above the standard quantum limit and observed quadrature distribution has additional Gaussian noise upon the minimum uncertainty Gaussian wavepacket [8]. Thus, the security analysis including experimental imperfections seems to become qualitatively different from that of the discrete schemes. * Electric address: namiki@qo.phys.gakushuin.ac.jpIn our previous work [9] we estimated G of a hybrid type scheme applying a postselection [8] for a given loss, provided Eve performs quadrature measurement for the lost part of the signal. In this case it is shown that G can be positive if the loss is less...