Millisecond pulsars (hereafter MSPs) differ from ordinary radio pulsars by much shorter spin periods P, smaller period derivatives $\dot{P}$ , higher dynamical ages $\tau$ , weaker magnetic fields B, and evolution histories (see, e.g., recent review by Lorimer 2001). Contrary to ordinary pulsars, only 9 of 56 MSPs currently known in the Galactic disk and 25 of 52 MSPs found in globular clusters are isolated objects (Lorimer 2001; Lorimer et al. 2002; Possenti et al. 2001). It is believed that the fast rotation of these neutron stars (NSs) was gained in the past by angular momentum transfer during mass accretion from a companion star (Bhattacharya & van den Heuvel 1991). This was supported by the discoveries of three accretion-powered X-ray MSPs in low-mass X-ray binaries (e.g., SAX J1808.4-3658, see Wijnands & van der Klis 1998).

**Table 1:** Parameters of PSR J0030+0451 (Lommen et al. 2000; Becker et al. 2000, unless specified otherwise).
$\begin{displaymath}\begin{tabular}{ccccccccccc} \hline\hline \multicolumn{6}{c}{... ...\vrule height 2.5ex width 0ex depth 0ex\\ \hline \end{tabular}\end{displaymath}$

Despite these differences, the distribution of integrated radio luminosities, as well as the luminosity dependence on P, $\dot{P}$ , B, and spindown energy losses $\dot{E}$ , are apparently similar for these much older and low-magnetized NSs, and for ordinary pulsars (Kuzmin & Losovsky 2001). About a dozen radio MSPs have been detected in X-rays. It is remarkable that their efficiency in converting spindown energy to X-ray luminosity is roughly the same as for ordinary pulsars, $L_{\rm X}/\dot{E}\sim 10^{-3}$ (Becker & Trümper 1997; Becker et al. 2000). This suggests that the emission mechanisms responsible for the multi-wavelength radiation of MSPs and ordinary pulsars can be similar, and one could therefore expect to detect MSPs in other spectral ranges as well, as has been done for several ordinary pulsars. Detection of the first MSP in gamma-rays (Kuiper et al. 2000) supports this idea. To our knowledge, there are still no reports on optical detection of isolated MSPs. It is hardly possible to detect thermal emission from the entire surface of these old, 10⁸-10¹⁰ yr, and cold NSs. However, the spindown energy, expected to power the nonthermal emission of pulsars, can be much higher for MSPs than for old ordinary pulsars, and may even rival that of young pulsars. Assuming the same efficiency of conversion of spindown energy to nonthermal optical luminosity as for ordinary pulsars, one can estimate that nearby MSPs may well be detectable in the optical with large telescopes. A problem is, however, that most of the nearby and energetic MSPs are components of close binary systems where the companion is predominantly either a white dwarf or main sequence star (Lorimer 2001) which outshines the pulsar in the optical. Fortunately, there are at least nine solitary MSPs in Galactic disk whose companions are believed to have been either evaporated or ablated (see, e.g., Lommen et al. 2000).

Here we report on deep BVR imaging of the field of one of these solitary millisecond pulsars, PSR J0030+0451. This pulsar was only recently discovered with the Arecibo telescope (Lommen et al. 2000), and soon thereafter detected in X-rays during the final observations with the ROSAT/PSPC (Becker et al. 2000). Recently it was re-observed in X-rays with the XMM-Newton (Becker & Aschenbach 2002). This relatively nearby NS (see Table 1 for its parameters) is characterized by high X-ray flux, about $(4.3{-}6.8)\times10^{-13}$ erg s^-1 cm^-2 in the 0.1-2.4 keV band, and low interstellar absorption, $N_{\rm H}\la 3\times10^{20}$ cm^-2, corresponding to a color excess $E(B-V)\la 0.06$ mag. This makes it a promising candidate for optical detection. In Sect. 2 we present the observations and the data reduction. In Sect. 3 we discuss our results in the optical in conjunction with the available X-ray data.

1 Introduction