Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose-Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.

We follow the evolution of the elementary excitations of the quantum antiferromagnet TlCuCl3 through the pressure-induced quantum critical point, which separates a dimer-based quantum disordered phase from a phase of long-ranged magnetic order. We demonstrate by neutron spectroscopy the continuous emergence in the weakly ordered state of a low-lying but massive excitation corresponding to longitudinal fluctuations of the magnetic moment. This mode is not present in a classical description of ordered magnets, but is a direct consequence of the quantum critical point.Although quantum fluctuations of both spin and charge degrees of freedom are the key to the essential physics of many challenging problems in condensed matter systems, the microscopic control of zero-point fluctuations has to date remained largely a theoretical abstraction. However, full control over the interaction parameters can now be effected in cold atomic condensates through the standing-wave amplitudes of the optical lattice. Similarly, in quantum magnets the exchange interactions can be controlled by the application of pressure, altering the effect of spin fluctuations. We follow this approach to investigate the physics of a quantum system whose fluctuations are "tuned" in a continuous way.The most dramatic manifestation of such control is the driving of a quantum phase transition [QPT, Fig. 1(a)] between two different ground states [1]. Structurally dimerized S = 1/2 spin systems offer a particularly clean realization both of the magnetic field-induced QPT, which has been studied extensively in a number of materials [2], and of the qualitatively different magnetic QPT driven by hydrostatic pressure [3]. The Hamiltonian

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