Resolving Vacuum Fluctuations in an Electrical Circuit by Measuring the Lamb Shift

Quantum theory predicts that empty space is not truly empty. Even in the absence of any particles or radiation, in pure vacuum, virtual particles are constantly created and annihilated. In an electromagnetic field, the presence of virtual photons manifests itself as a small renormalization of the energy of a quantum system, known as the Lamb shift. We present an experimental observation of the Lamb shift in a solid-state system. The strong dispersive coupling of a superconducting electronic circuit acting as a quantum bit (qubit) to the vacuum field in a transmission-line resonator leads to measurable Lamb shifts of up to 1.4% of the qubit transition frequency. The qubit is also observed to couple more strongly to the vacuum field than to a single photon inside the cavity, an effect that is explained by taking into account the limited anharmonicity of the higher excited qubit states.

[1]  J. Raimond,et al.  From Lamb shift to light shifts: Vacuum and subphoton cavity fields measured by atomic phase sensitive detection. , 1994, Physical review letters.

[2]  Alexander Shnirman,et al.  Cavity QED in superconducting circuits: susceptibility at elevated temperatures , 2004 .

[3]  A. Siegert,et al.  Magnetic Resonance for Nonrotating Fields , 1940 .

[4]  K. Schwab,et al.  Quantum measurement of a coupled nanomechanical resonator–Cooper-pair box system , 2003, cond-mat/0301252.

[5]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[6]  Jens Koch,et al.  Controlling the spontaneous emission of a superconducting transmon qubit. , 2008, Physical review letters.

[7]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[8]  S. Girvin,et al.  Wiring up quantum systems , 2008, Nature.

[9]  A. Wallraff,et al.  Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system , 2008, Nature.

[10]  Stephan W Koch,et al.  Vacuum Rabi splitting in semiconductors , 2006 .

[11]  J. Teufel,et al.  Measuring nanomechanical motion with a microwave cavity interferometer , 2008, 0801.1827.

[12]  P. Shukla.  Stopping power of a charged dust projectile in the presence of the dust acoustic wave in dusty plasmas , 2007 .

[13]  Willis E. Lamb,et al.  Fine Structure of the Hydrogen Atom by a Microwave Method , 1947 .

[14]  H. Bethe.  The Electromagnetic shift of energy levels , 1947 .

[15]  S. Girvin,et al.  Erratum: ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field [Phys. Rev. Lett. 94 , 123602 (2005)] , 2007 .

[16]  R. J. Schoelkopf,et al.  Resolving photon number states in a superconducting circuit , 2007, Nature.

[17]  Peter W. Milonni,et al.  The Quantum Vacuum: An Introduction to Quantum Electrodynamics , 1993 .

[18]  Jens Koch,et al.  Suppressing Charge Noise Decoherence in Superconducting Charge Qubits , 2007, 0712.3581.

[19]  Heinzen,et al.  Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator. , 1987, Physical review letters.

[20]  Alex I. Braginski,et al.  The SQUID handbook , 2006 .

[21]  Jun Ye,et al.  Quantum State Engineering and Precision Metrology Using State-Insensitive Light Traps , 2008, Science.

[22]  H. Casimir,et al.  The Influence of Retardation on the London-van der Waals Forces , 1948 .

[23]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.

[24]  H. Walther,et al.  Quantum Electrodynamic Shifts of Rydberg Energy Levels between Parallel Metal Plates , 1998 .

[25]  Alexandre Blais,et al.  Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting , 2006 .

[26]  Julian Schwinger,et al.  Selected papers on quantum electrodynamics , 1958 .

[27]  Salomon,et al.  Measurement of the hydrogen 1S- 2S transition frequency by phase coherent comparison with a microwave cesium fountain clock , 2000, Physical review letters.